A356442 a(n) is the least positive even number that is the unordered sum of two primes congruent mod 10 in exactly n ways.

2, 4, 26, 86, 126, 174, 264, 324, 396, 456, 546, 594, 624, 876, 966, 984, 924, 954, 1326, 1344, 1386, 1512, 1596, 1638, 1848, 1764, 2046, 2226, 2838, 2574, 2706, 2604, 2772, 2436, 3366, 3066, 2964, 3432, 3894, 3738, 3234, 3696, 3654, 4074, 4446, 4158, 4368, 4494, 4788, 5016, 4746, 5754, 4914

Offset: 0

Author

J. M. Bergot and Robert Israel, Aug 07 2022

Keywords

• nonn
• base

Comments

a(n) is the least even number k such that there are exactly n unordered pairs of primes (p,q) with p + q = k and p and q have the same last decimal digit.

Examples

			a(3) = 86 because 86 = 3 + 83 = 13 + 73 = 43 + 43, all summands being prime with last digit 3, and 86 is the least even number that works.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A023036.

Programs

Maple

f:= proc(m) local d, p;
  if m mod 10 = 0 then return 0 fi;
  d:= chrem([m/2 mod 5, 1],[5,2]);
  nops(select(p -> isprime(p) and isprime(m-p), [seq(p,p=d..m/2,10)]))
end proc:
f(4):= 1:
M:= 100: # to get a(0)..a(M)
V:= Array(0..M): count:= 0:
for m from 2 by 2 while count < M+1 do
  v:= f(m);
  if v <= M and V[v] = 0 then V[v]:= m; count:= count+1 fi
od:
convert(V,list);