A351826 a(n) is the least k such that there are exactly n positive numbers j such that k - 2^j and k + 2^j are both prime.

1, 5, 9, 15, 75, 165, 16065, 137445, 540645, 2222535, 374958045, 18327149295

Offset

0,2

Comments

All terms are odd. If the number j is allowed to be 0, then a(1) = 4. - Chai Wah Wu, Mar 24 2022

Links

Table of n, a(n) for n=0..11.

Example

a(4) = 75 because 75 +/- 2^2 = 79 and 71, 75 +/- 2^3 = 83 and 67, 75 +/- 2^5 = 107 and 43, and 75 +/- 2^6 = 139 and 11 are all prime, and 75 is the least number for which there are exactly 4 such powers of 2.

Maple

f:= proc(n) local t, s:
   nops(select(t -> isprime(n+2^t) and isprime(n-2^t), [$1..ilog2(n)]));
end proc:
V:= Array(0..10): count:= 0:
for n from 1 while count < 11 do
  v:= f(n); if V[v] = 0 then V[v] := n; count:= count+1 fi
od:
convert(V, list);

Prog

(Python)
from itertools import count
from sympy import isprime
def A351826(n):
    for k in count(1, 2):
        c = 0
        for j in count(1):
            if k-2**j < 2:
                break
            if isprime(k-2**j) and isprime(k+2**j):
                c += 1
            if c > n:
                break
        if c == n: return k # Chai Wah Wu, Mar 24 2022

Crossrefs

Sequence in context: A249331 A345953 A075133 * A066081 A076856 A242973

Adjacent sequences: A351823 A351824 A351825 * A351827 A351828 A351829

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Mar 24 2022

Extensions

a(11) from Jean-Marc Rebert, Mar 31 2022

Status

approved