A247342 Let b_k=3...3 consist of k>=1 3's. Then a(n) is the smallest k such that the odd part (A000265) of concatenation b_k 2^n is prime, or a(n)=0 if there is no such prime.

1, 2, 1, 1, 1, 1, 4, 3, 2, 1, 3, 1, 1, 6, 1, 1, 1, 3, 1, 15, 29, 5, 1, 2, 3, 6, 1, 6, 20, 6, 3, 50, 3, 22, 8, 5, 5, 1, 84, 8, 7, 36, 3, 6, 7, 20, 6, 6, 8, 1, 6, 3, 2, 38, 1, 5, 3, 2, 5, 16, 1, 12, 13, 7, 1, 4, 16, 5, 32, 1, 6, 13, 4, 150, 7, 29, 17, 9, 12, 34

Offset

0,2

Comments

Conjecture: for all n, a(n)>0.

a(443) > 17000 if it is not 0.

Links

Robert Israel, Table of n, a(n) for n = 0..442

Example

2^0=1 and already 31 is prime. So a(0)=1;
2^1=2, but odd part of 32 is 1 (nonprime); then consider odd part of 332. It is 83 that is prime. So a(1)=2.

Maple

f:= proc(n) local m, d, k, x;
    m:= 2^n;
    d:=ilog10(m);
    for k from 1 do
       x:= (10^k-1)/3*10^(d+1)+m;
       if isprime(x/2^padic:-ordp(x, 2)) then return k fi
    od
end proc:
map(f, [$0..100]); # Robert Israel, Oct 30 2016

Prog

(PARI) a(n) = {k = 0; while (! ((val = eval(concat(Str((10^k-1)/3), Str(2^n)))) && isprime(val/2^valuation(val, 2))), k++); k; } \\ Michel Marcus, Sep 15 2014

Crossrefs

Cf. A000079, A232210, A242775, A247341.

Sequence in context: A337131 A046876 A026584 * A174547 A119326 A219866

Adjacent sequences: A247339 A247340 A247341 * A247343 A247344 A247345

Keyword

nonn,base

Author

Vladimir Shevelev, Sep 14 2014

Extensions

More terms from Michel Marcus, Sep 15 2014

Status

approved