

A208091


Smallest number m such that exactly n primes of the form 2^m  2^k  1 exist, 1 <= k < m.


2



1, 11, 3, 4, 6, 8, 38, 24, 32, 18, 48, 138, 20, 588, 144, 252, 5520, 168, 7200, 2400, 2850
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OFFSET

0,2


COMMENTS

A208083(a(n)) = n and A208083(m) <> n for m < a(n).
a(21) > 7600, if it exists.  Giovanni Resta, Jun 14 2018


LINKS

Table of n, a(n) for n=0..20.


EXAMPLE

a(3) = 4 because for m = 4 there are exactly three primes of the given form: 13 = 2^4  2^1  1, 11 = 2^4  2^2  1, 7 = 2^4  2^3  1 and no smaller m satisfies this requirement.


MAPLE

f:= n > nops(select(k > isprime(2^n2^k1), [$1..n1])):
for n from 1 to 300 do
v:= f(n);
if not assigned(A[v]) then A[v]:= n fi;
od:
seq(A[m], m=0..15); # Robert Israel, Jun 13 2018


MATHEMATICA

A = <>; Do[c = Length@Select[Range[n1], PrimeQ[2^n  2^#  1] &]; If[! KeyExistsQ[A, c], A[c]=n], {n, 140}]; Array[A, 13, 0] (* Giovanni Resta, Jun 13 2018 *)


PROG

(Haskell)
import Data.List (elemIndices, elemIndex)
import Data.Maybe (fromJust)
a208091 = (+ 1) . fromJust . (`elemIndex` a208083_list)
(PARI) a(n) = {my(m=1); while(sum(k=1, m, isprime(2^m2^k1)) != n, m++); m; } \\ Michel Marcus, Jun 13 2018


CROSSREFS

Cf. A208083.
Sequence in context: A309389 A110089 A177415 * A070695 A070720 A010189
Adjacent sequences: A208088 A208089 A208090 * A208092 A208093 A208094


KEYWORD

nonn,more


AUTHOR

Reinhard Zumkeller, Feb 23 2012


EXTENSIONS

Corrected by Robert Israel, Jun 13 2018
a(17), a(19)a(20) from Robert Israel, Jun 13 2018
a(16), a(18) from Giovanni Resta, Jun 14 2018


STATUS

approved



