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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(m-2)) + A006530(b(m-1)); 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 (list; graph; refs; listen; history; text; internal format)
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[n-1]][[-1, 1]]+FactorInteger[h[n-2]][[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[n-2])+A006530(bvec[n-1]); if(4==bvec[n], return(n-1))); }; \\ 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

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Last modified May 28 16:37 EDT 2022. Contains 354119 sequences. (Running on oeis4.)