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A345224 a(n) is the least prime p such that there are exactly n primes of the form p+2^k for 2^k < p. 1
61, 2, 11, 67, 149, 2081, 5651, 11831, 51479, 536279, 3058871, 11894801, 106446433 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..12.

FORMULA

A345238(A000720(a(n))) = n.

EXAMPLE

a(3) = 67 because 67+2^2 = 71, 67+2^4 = 83 and 67+2^6 = 131 are primes, and 67 is the least prime that produces exactly 3 primes in this way.

MAPLE

f:= proc(p) local k;

  nops(select(isprime, [seq(p+2^k, k=1..ilog2(p))]))

end proc:

f(2):= 1

V:= Array(0..11):

count:= 0:

p:= 1:

while count < 12 do

  p:= nextprime(p);

  v:= f(p);

  if V[v] = 0 then V[v]:= p; count:= count+1

  fi

od:

convert(V, list);

MATHEMATICA

Table[p=1; While[Length@Select[Table[Prime@p+2^k, {k, 0, Floor[Log2@Prime@p]}], PrimeQ]!=n, p++]; Prime@p, {n, 0, 9}] (* Giorgos Kalogeropoulos, Jun 11 2021 *)

CROSSREFS

Cf. A000720, A345238.

Sequence in context: A241601 A132096 A051322 * A198189 A102600 A316918

Adjacent sequences:  A345221 A345222 A345223 * A345225 A345226 A345227

KEYWORD

nonn,more

AUTHOR

J. M. Bergot and Robert Israel, Jun 11 2021

STATUS

approved

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Last modified June 30 02:41 EDT 2022. Contains 354913 sequences. (Running on oeis4.)