

A271720


a(1)=1; for n>1, define a sequence {b(m), m >= 1} by b(1)=n b(2)=13, and b(m) = A020639(b(m2)) + A006530(b(m1)); then a(n) is the number of terms in that sequence before the first of the infinite string of 4s.


1



8, 13, 15, 13, 4, 13, 12, 13, 15, 13, 4, 13, 16, 13, 15, 13, 12, 13, 15, 13, 15, 13, 4, 13, 4, 13, 15, 13, 8, 13, 12, 13, 15, 13, 4, 13, 12, 13, 15, 13, 4, 13, 8, 13, 15, 13, 12, 13, 12, 13, 15, 13, 12, 13, 4, 13, 15, 13, 4, 13, 8, 13, 15, 13, 4, 13, 12, 13, 15, 13, 8, 13, 11, 13, 15, 13, 12, 13
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OFFSET

1,1


COMMENTS

Note that the majority of the terms (every other term, initially) are equal to b(2), which is 13. This happens with several other values of b(2) less than 20. Many other values for b(2) have been tested, and it seems that for all b(2) < 100000000, a(n) < 20.
Records 8, 13, 15, 16, 19, 20, 24, ... occur at 1, 2, 3, 13, 349, 3919, 55633, ...


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537


EXAMPLE

n = 6; the sequence is:
6, 13, 15, 18, 6, 5, 7, 12, 10, 7, 9, 10, 8, 4, 4, 4, ...
There are 13 terms before the first of the infinite 4s; a(6) = 13.
For n = 55633 the sequence is: 55633, 13, 55646, 27836, 6961, 6963, 7172, 166, 85, 19, 24, 22, 13, 15, 18, 6, 5, 7, 12, 10, 7, 9, 10, 8, 4, 4, 4, ... . As the first 4 comes as the 25th term, a(55633) = 24.  Antti Karttunen, Oct 01 2018


MATHEMATICA

Table[
Clear[h];
h[1]=x;
h[2]=13;
h[n_]:=FactorInteger[h[n1]][[1, 1]]+FactorInteger[h[n2]][[1, 1]];
Position[Array[h, 100], 4][[1, 1]]1,
{x, 1, 100}] (*This only works for x≠4*)


PROG

(PARI)
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1); \\ From A006530
A020639(n) = if(1==n, n, factor(n)[1, 1]);
A271720(n) = { my(up=1001, bvec = vector(up), m=1); bvec[1] = n; bvec[2] = 13; for(n=3, oo, bvec[n] = A020639(bvec[n2])+A006530(bvec[n1]); if(4==bvec[n], return(n1))); }; \\ Antti Karttunen, Oct 01 2018


CROSSREFS

Sequence in context: A253775 A168137 A252458 * A243436 A214412 A080361
Adjacent sequences: A271717 A271718 A271719 * A271721 A271722 A271723


KEYWORD

nonn


AUTHOR

Cody M. Haderlie, Apr 12 2016


STATUS

approved



