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A263046 Smallest number k>2 such that k*2^n + 1 is a prime number. 1
4, 3, 3, 5, 6, 3, 3, 5, 3, 15, 12, 6, 3, 5, 4, 5, 12, 6, 3, 11, 7, 11, 25, 20, 10, 5, 7, 15, 12, 6, 3, 35, 18, 9, 12, 6, 3, 15, 10, 5, 6, 3, 9, 9, 15, 35, 19, 27, 15, 14, 7, 14, 7, 20, 10, 5, 27, 29, 54, 27, 31, 36, 18, 9, 12, 6, 3, 9, 31, 23, 39, 39, 40, 20, 10, 5, 58 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

If k = 2^j then 2^(n+j) + 1 is a Fermat prime.

a(n) = 3 if and only if 3*2^n + 1 is a prime; that is, n belongs to A002253. - Altug Alkan, Oct 08 2015

a(n+1) >= ceiling(a(n)/2). If a(n) is even then a(n+1) = a(n)/2. - Robert Israel, Oct 08 2015

LINKS

Pierre CAMI, Table of n, a(n) for n = 0..10000

EXAMPLE

3*2^1 + 1 = 7 (prime), so a(1)=3:

3*2^2 + 1 = 13 (prime), so a(2)=3;

3*2^3 + 1 = 25 (composite), 4*2^3 + 1 = 33 (composite), 5*2^3 - 1 = 41 (prime), so a(3)=5.

MAPLE

f:= proc(n) local k;

    for k from 3 do if isprime(k*2^n+1) then return k fi od

  end proc:

seq(f(n), n=1..100); # Robert Israel, Oct 08 2015

MATHEMATICA

Table[k = 3; While[! PrimeQ[k 2^n + 1], k++]; k, {n, 76}] (* Michael De Vlieger, Oct 08 2015 *)

PROG

(PARI) a(n) = {k=3; while (! isprime(k*2^n+1), k++); k; } \\ Michel Marcus, Oct 08 2015

CROSSREFS

Cf. A247479, A262994.

Sequence in context: A063571 A005589 A052360 * A154913 A154915 A238376

Adjacent sequences:  A263043 A263044 A263045 * A263047 A263048 A263049

KEYWORD

nonn

AUTHOR

Pierre CAMI, Oct 08 2015

STATUS

approved

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Last modified June 26 10:12 EDT 2019. Contains 324375 sequences. (Running on oeis4.)