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 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 (list; graph; refs; listen; history; text; internal format)
 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 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: 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

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Last modified September 20 16:48 EDT 2019. Contains 327242 sequences. (Running on oeis4.)