A078671 Number of times the n-th prime appears among the decimal digits of 2^(2^n) + 1, the Fermat numbers.

0, 0, 1, 1, 0, 0, 1, 1, 2, 4, 9, 14, 21, 46, 112, 204, 374, 809, 1586, 3237, 6385, 12539, 25637, 50603, 100891, 20382, 40281, 81405, 161718, 323703, 645928

Offset

1,9

Comments

Conjectures: Is a(n) monotonically increasing for n > 4? Does lim{n->inf} a(n)/a(n+1) = 0.5? - Ryan Propper, Jan 04 2008

Links

Table of n, a(n) for n=1..31.

Example

a(4)=1 because the 4th prime 7 appears once in 2^2^4 + 1 = 65537.

Prog

(PARI) \ Type ff to run. {mcf(d, n)=local(a, c=0, L); L=length(Str(d)); if(L>1, a=2, a=1); while(n>0, if(n%(10^a)==d, n=floor(n/10); c++, n=floor(n/10); )); c } {ff()=local(a); print("Enter an ending value <= 25: "); a=input(); if(a>25, error("Input not valid, try again."), for(n=1, a, print1(mcf(prime(n), (2^2^n+1))", ")); ) }

Crossrefs

Cf. A000215.

Sequence in context: A190553 A270532 A281407 * A119637 A169762 A291465

Adjacent sequences: A078668 A078669 A078670 * A078672 A078673 A078674

Keyword

base,more,nonn

Author

Jason Earls, Dec 16 2002

Extensions

More terms from Ryan Propper, Jan 04 2008

a(24)-a(26) from Donovan Johnson, Nov 17 2008

Correction of a(26). a(27)-a(31) from Robert Gerbicz, Nov 24 2010

Status

approved