cp's OEIS Frontend

A305825 Number of different ways that a number between two members of a twin prime pair can be expressed as a sum of two smaller such numbers.

%I A305825 #44 Jun 20 2024 10:04:52
%S A305825 0,0,0,1,1,1,1,2,2,1,1,2,3,2,3,1,4,3,3,3,2,6,3,5,3,3,3,3,3,8,4,2,3,3,
%T A305825 6,4,4,6,7,8,3,6,3,9,8,6,7,5,8,4,1,5,6,3,7,1,6,6,4,8,1,5,5,8,9,11,10,
%U A305825 6,8,16,13,9,12,6,7,8,4,16,9,6,13,10,9,5,6,6
%N A305825 Number of different ways that a number between two members of a twin prime pair can be expressed as a sum of two smaller such numbers.
%C A305825 Number of pairs i, j such that A014574(i) + A014574(j) = A014574(n) where 1 <= i <= j < n. - _David A. Corneth_, Aug 05 2018
%e A305825 a(8)=2 because the 8th isolated composite number is 72 = 60 + 12 and 42 + 30 with (12,30,42,60) all isolated composite numbers.
%o A305825 (PARI) lista(nn) = {my(vc = select(x->(isprime(x-1) && isprime(x+1)), [1..nn])); for (n=1, #vc, nb = 0; for (j=1, n, for (k=j+1, n, if (vc[j]+vc[k] == vc[n], nb++));); print1(nb, ", "););} \\ _Michel Marcus_, Jul 05 2018
%o A305825 (PARI) first(n) = {my(isolated = List(), isomap = Map, res = vector(n), k, q = 3); forprime(p = 5, , if(p - q == 2, listput(isolated, q+1); mapput(isomap, q+1, #isolated); if(#isolated == n, break)); q = p); for(i = 1, #isolated, for(j = 1, i - 1, diff = isolated[i] - isolated[j]; if(diff < isolated[j], if( mapisdefined(isomap, diff, &k), res[i]++), next(1)))); res} \\ _David A. Corneth_, Aug 05 2018
%Y A305825 Cf. A014574, A134143.
%K A305825 nonn
%O A305825 1,8
%A A305825 _Pedro Caceres_, Jun 10 2018
%E A305825 Name changed, extended data by _David A. Corneth_, Aug 05 2018