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
Keywords
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
Programs
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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