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

1,8

Comments

Number of pairs i, j such that A014574(i) + A014574(j) = A014574(n) where 1 <= i <= j < n. - David A. Corneth, Aug 05 2018

Links

Table of n, a(n) for n=1..86.

Example

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.

Prog

(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

Crossrefs

Cf. A014574, A134143.

Sequence in context: A025863 A346307 A339352 * A366780 A324029 A334046

Adjacent sequences: A305822 A305823 A305824 * A305826 A305827 A305828

Keyword

nonn

Author

Pedro Caceres, Jun 10 2018

Extensions

Name changed, extended data by David A. Corneth, Aug 05 2018

Status

approved