A269026 a(1)=1; for n>1, define a sequence {b(m), m >= 1} by b(1)=a(n-1), b(2)=n, 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, 9, 12, 1, 4, 10, 5, 6, 8, 6, 5, 3, 15, 7, 12, 2, 17, 7, 4, 6, 13, 11, 8, 10, 9, 3, 12, 9, 11, 3, 12, 2, 16, 6, 12, 10, 5, 11, 12, 6, 9, 7, 12, 14, 13, 11, 16, 10, 5, 7, 12, 14, 8, 10, 5, 11, 4, 10, 17, 15, 15, 7, 8, 2, 5, 3, 15, 7, 4, 9, 12, 10, 5, 10, 13, 3, 11, 11, 11

Offset: 1

Author

Cody M. Haderlie, Apr 11 2016

Keywords

• nonn

Examples

			n = 3:
a(n-1) = a(2) = 9;
b(1) = 9, b(2) = 3;
the sequence generated is: 9, 3, 6, 6, 5, 7, 12, 10, 7, 9, 10, 8, 4, 4, 4, ...
There are 12 terms before the first of the infinite 4s, so a(3) = 12.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A020639, A271621.

Programs

PARI

spf(n) = if (n==1, 1, vecmin(factor(n)[,1]));
gpf(n) = if (n==1, 1, vecmax(factor(n)[,1]));
nbt(a, n) = {x = a; y = n; nb = 0; while (!((x==4) && (y==4)), z = spf(x) + gpf(y); x = y; y = z; nb++;); nb;}
lista(nn) = { print1(a=1, ", "); for (n=2, nn, na = nbt(a, n); print1(na, ", "); a = na;);} \\ Michel Marcus, Apr 12 2016