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.
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, 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, 6, 8, 16, 13, 9, 12, 6, 7, 8, 4, 16, 9, 6, 13, 10, 9, 5, 6, 6
Offset: 1
Keywords
Examples
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.
Programs
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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 -
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
Extensions
Name changed, extended data by David A. Corneth, Aug 05 2018
Comments