A243624 Numbers that are the sum of 2 different primes, with repetitions.

5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 16, 18, 18, 19, 20, 20, 21, 22, 22, 24, 24, 24, 25, 26, 26, 28, 28, 30, 30, 30, 31, 32, 32, 33, 34, 34, 34, 36, 36, 36, 36, 38, 39, 40, 40, 40, 42, 42, 42, 42, 43, 44, 44, 44, 45, 46, 46, 46, 48, 48, 48, 48, 48, 49, 50, 50, 50, 50, 52, 52, 52, 54, 54, 54, 54, 54, 55, 56, 56, 56, 58, 58, 58

Offset: 1

Author

Zak Seidov, Mar 07 2015

Keywords

• nonn

Examples

			16=3+13=5+11 hence 16 occurs twice.
24=5+19=7+13=11+13 hence 24 occurs 3 times.
50=p+q with {p,q}={{3,47},{7,43},{13,37},{19,31}}, 4 representations.
48=p+q with {p,q}={{5,43},{7,41},{11,37},{17,31},{19,29}}, 5 representations.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014091, A038609.

Programs

Maple

f:= proc(n) local i;
    if n::odd then
      if isprime(n-2) then n else NULL fi
    else
      n$nops(select(t -> isprime(t) and isprime(n-t), [seq(i,i=3..floor((n-1)/2), 2)]))
    fi
end proc:
map(f, [$5..100]); # Robert Israel, Mar 09 2025

Mathematica

Flatten[Table[Table[n,Count[IntegerPartitions[n,{2}],?(AllTrue[#,PrimeQ]&&#[[1]]!=#[[2]]&)]],{n,60}]] (* _Harvey P. Dale, Jun 20 2025 *)