

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, 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
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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(x1) && 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: A161638 A066030 A025863 * A324029 A136605 A165621
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



