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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 16:24 EDT 2021. Contains 347528 sequences. (Running on oeis4.)