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.

61, 2, 11, 67, 149, 2081, 5651, 11831, 51479, 536279, 3058871, 11894801, 106446433

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