cp's OEIS Frontend

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

%I A243624 #29 Jun 20 2025 15:38:28
%S A243624 5,7,8,9,10,12,13,14,15,16,16,18,18,19,20,20,21,22,22,24,24,24,25,26,
%T A243624 26,28,28,30,30,30,31,32,32,33,34,34,34,36,36,36,36,38,39,40,40,40,42,
%U A243624 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
%N A243624 Numbers that are the sum of 2 different primes, with repetitions.
%H A243624 Robert Israel, <a href="/A243624/b243624.txt">Table of n, a(n) for n = 1..10000</a>
%e A243624 16=3+13=5+11 hence 16 occurs twice.
%e A243624 24=5+19=7+13=11+13 hence 24 occurs 3 times.
%e A243624 50=p+q with {p,q}={{3,47},{7,43},{13,37},{19,31}}, 4 representations.
%e A243624 48=p+q with {p,q}={{5,43},{7,41},{11,37},{17,31},{19,29}}, 5 representations.
%p A243624 f:= proc(n) local i;
%p A243624     if n::odd then
%p A243624       if isprime(n-2) then n else NULL fi
%p A243624     else
%p A243624       n$nops(select(t -> isprime(t) and isprime(n-t), [seq(i,i=3..floor((n-1)/2), 2)]))
%p A243624     fi
%p A243624 end proc:
%p A243624 map(f, [$5..100]); # _Robert Israel_, Mar 09 2025
%t A243624 Flatten[Table[Table[n,Count[IntegerPartitions[n,{2}],_?(AllTrue[#,PrimeQ]&&#[[1]]!=#[[2]]&)]],{n,60}]] (* _Harvey P. Dale_, Jun 20 2025 *)
%Y A243624 Cf. A014091, A038609.
%K A243624 nonn
%O A243624 1,1
%A A243624 _Zak Seidov_, Mar 07 2015