Repeating Sequence-Rejoinder

This is with reference to my earlier blog with the same title.
I had shown a sequence with a few numbers--0,0,0,1,0,2,1,0,3,2,1,4,0,5,3,2,6,1,4......By deleting each number like 0,1,2,3,4 etc etc first occurring in it,the same sequence will be revealed.
I have worked further on it and have found further digits upto the 143rd place.I have shown below the sequence in successive rows -each row starting with 0.
0..........................................................................................contains 1 number
0..........................................................................................contains 1.number.
0,1.......................................................................................contains 2 numbers
0,2,1....................................................................................contains 3 numbers
0,3,2,1,4...............................................................................contains 5 numbers
0,5,3,2,6,1,7,4......................................................................contains 8 numbers
0,8,5,3,9,2,10,6,1,11,7,4,12.................................................contains 13 numbers
0,13,8,5,14,3,15,9,2,16,10,6,17,1,18,11,7,19,4,20,12.........contains 21 numbers
0,21,13,8,22,5,23,14,3,24,15,9,25,2,26,16,10,27,6,28,17,1,29,18
                11,30,7,31,19,4,32,20,12,33................................contains 34 numbers.
The total no of items in each group is 1,1,2,3,5,8,13,21,34..These numbers are part of a sequence called Fibonnaci number sequence,where starting from the 3rd item the successive numbers work out as the sum of the previous 2 numbers.
The next group which should contain 55 items(21+34) has not been shown by me.This group also starts with 0 (like the previous groups)and contains 33 as the last item.
In the full sequence,the digit 1 occurs at places   4,7,11,18,29,47,76,123  etc etc.Call this group A
The digit 2 occurs at places 6,10,16,26,42,68,110 etc.etc.Call this group B
In both these groups cach number commencing from the 3rd works out as the sum of the previous 2 numbers..Likewise you can have groups for digits 3,4,5,6 etc etc.
A small digression  relating to digits/numbers occuring at various places-one sample-
In the full sequence the number 13 occurs at place 35 for the first time.
                                               18            at place 48
                                               26            at place 69
                                         and 39           at place 103.
You can see that the differences regarding the number and the places are 5,8,13 and 13,21,34 which are numbers in the Fibonnaci sequence.The next numbers in this sequence are 55 and 89.
So you will find that the number 60 (which is 21 places above 39) will occur at place 158(which is 55 more than 103).Similarly 94 (which is 34 places above 60)will occur first at place 247(which is 89 more than 158). 

Prime numbers-in several forms

Take the number 1373
This has an interesting feature
Take each digit,or take two digits at a time in the same order,or 3 digits at a time in the same order or all 4 digits together they are all primes viz
1,3,7,3
13,37,73
137,373
1373 -all are primes
Can you find some more 4 digit numbers like this? 

Collecting numbers for particular sums-2

 This is  a rejoinder to my earlier blog with same title.
There has been no response although it is a simple problem of logic
For exnmple instead of collecting 6 numbers from group A,you can consider removing 2 numbers from that group. Same logic with group B
Following are the solutions
Group A-total 220- by removing 55 and 11....group B-total 110- by removing 38 and 49
Group A-total 228-by removing 17 and 41....group B-total 114-by removing  45 and 38
Group A-total 234-by removing 11 and 41....group B-total 117-by removing  31 and 49
Is it not simple?

Finding square numbers-2

This is a rejoinder to my blog same title
I suggested you find a square number starting with five 2s
A number of that type is 2222219285521 which is a square of 1490711
You will find the square of 1490712 is 2222222266944
Also the square of 1490713 is 2222225248369 

Prime pyramid-adjacent primes-2

This is with reference to my earlier blog-same title
I had shown row 8 as follows-1,6,7,4,3,2,5,8 where each pair of adjacent numbers add upto a prime viz 1+6=7,6+7=13,7+4=11,4+3=7,3+2=5,2+5=7,5+8=13
The further rows can be formed as follows-
a)As 8+9=17 (a prime) ,we can simply add 9 to get 1,6,7,4,3,2,5,8,9
b)As 9+10=19(a prime),we can simply add 10 to get 1,6,7,4,3,2,5,8 ,9,10
c)As 10+11=21 which is not a prime we have to modify numbers in row (b)
For this we follow the same position upto 3,add the nos from 2 to 10 in the reverse way and then add 11
We will get 1,6,7,4,3,(10,9,8,5,2),11
d)12 can be added as 11+12=23,giving us 1,6,7,4,3,10,9,8,5,2,11,12
e)13 cannot be added as 12+13=25 is not a prime.The change is made as follows-
1,6,7,(12,11,2,5,8,9,10,3,4),13
Further rows are filled up in the same fashion-
f) 1,6,7,12,11,2,5,8,9,10,(13,4,3),14
h)1,6,7,12,11,2,5,8,9,10,13,4,3,14,15
j)1,6,7,12,11,2,5,8,9,10,13,4,3,14,15,16
k)1,6,7,12,11,2,5,8,9,10,13,4,3,(16,15,14),17
l)1,6,7,12,11,2,(17,14,15,16,3,4,13,10,9,8,5),18
m)1,6,7,12,11,2,17,14,15,16,3,4,13,10,9,8,5,18,19
n) 1,6,7,12,11,2,17,14,15,16,3,4,13,10,(19,18,5,8,9),20
We can follow the same procedure for further rows.  

Division one number by another-probability-rejoinder

 This is with reference to my previous blog where we consider any number A between 10 and 1000-remove the last digit to get number B-We wanted the probability of B evenly dividing A.
Total number of choices possible for A----1000-9=991
Following give correct divisibility by B-
1)All numbers ending with zero (like 450)---------109
2)All multiples of 11 below 100 (like 22,33 etc)-----8
3) Six other cases-24,26,28,36,39,48---------------6
Total----------------------------------------------123
The probability is hence 123/991

Finding square numbers

Everyone knows how to extract the square root of any number
My proposal here is to find a number which has certain specialities but is also a perfect square number
For instance you are asked to find a number starting with six 2's and which is a perfect square.
With a little work of trial and error you can find it.
My research gave the number 222222674025 which is the square of 471405
But suppose I ask you to find a square number starting with five 2's.Try to do a little math and find the number.
Will it be smaller than 222222674025 shown by me earlier?