A022920 Number of solutions to c(1)*prime(4) + ... + c(n)*prime(n+3) = 2, where c(i) = +-1 for i > 1, c(1) = 1.

0, 0, 0, 0, 0, 0, 0, 1, 0, 7, 0, 12, 0, 61, 0, 131, 0, 472, 0, 2039, 0, 5924, 0, 21095, 0, 76058, 0, 274023, 0, 1032989, 0, 3694643, 0, 12987172, 0, 48417270, 0, 174274092, 0, 642785629, 0, 2402825962, 0, 8918414212, 0, 32868915523, 0, 123145191037, 0

Offset

1,10

Comments

Each second entry is 0 because the primes that are involved are all odd and the right hand side is even. - R. J. Mathar, Aug 06 2015

Links

Alois P. Heinz, Table of n, a(n) for n = 1..500

Formula

a(2n-1) = 0 for all n >= 1.

Mathematica

b[n_, s_, p_] := b[n, s, p] = If[n <= s, If[s == p, Boole[n == s], b[Abs[n - p], s - p, NextPrime[p - 1, -1]] + b[n + p, s - p, NextPrime[p - 1, -1] ]], If[s <= 0, b[Abs[s], Sum[Prime[i], {i, p + 1, p + n - 1}], Prime[p + n - 1]]]] /. Null -> 0; a[n_] := b[n, 2 - Prime[4], 4]; Array[a, 50] (* Jean-François Alcover, Feb 14 2018, after M. F. Hasler *)

Prog

(PARI) A022920(n)={my(p=vector(n-1, i, prime(i+4))); sum(i=1, 2^(n-1), sum(j=1, #p, (1-bittest(i, j-1)<<1)*p[j], 7)==2)} \\ For illustrative purpose; too slow for n >> 20. - M. F. Hasler, Aug 08 2015
(PARI) a(n, s=2-prime(4), p=4)=if(n<=s, if(s==p, n==s, a(abs(n-p), s-p, precprime(p-1))+a(n+p, s-p, precprime(p-1))), if(s<=0, a(abs(s), sum(i=p+1, p+n-1, prime(i)), prime(p+n-1)))) \\ M. F. Hasler, Aug 09 2015

Crossrefs

Cf. A022894, A022895, A022896 (r.h.s. = 0, 1 & 2, using all primes), A083309 and A022897 - A022899 (using primes >= 3), A022900 - A022902 (using primes >=5), A022903, A022904 (r.h.s. = 0 & 1, using primes >= 7); A261061 - A261063 & A261045 (r.h.s. = -1); A261057, A261059, A261060 & A261044 (r.h.s. = -2).

Sequence in context: A122699 A262807 A169603 * A331423 A240825 A243773

Adjacent sequences: A022917 A022918 A022919 * A022921 A022922 A022923

Keyword

nonn

Author

Clark Kimberling

Extensions

Corrected by R. J. Mathar, Aug 06 2015

a(22)-a(49) from Alois P. Heinz, Aug 06 2015

Status

approved