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

1,2

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A006530, A020639, A271621.

Sequence in context: A159003 A352004 A196509 * A124606 A110647 A347943

Adjacent sequences: A269023 A269024 A269025 * A269027 A269028 A269029

Keyword

nonn

Author

Cody M. Haderlie, Apr 11 2016

Status

approved