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 A350404 Number of solutions to +-2 +- 3 +- 5 +- 7 +- ... +- prime(n) = 0 or 1. 4
 1, 0, 1, 2, 1, 2, 3, 4, 6, 10, 16, 26, 45, 78, 138, 244, 439, 784, 1417, 2572, 4698, 8682, 16021, 29720, 55146, 102170, 190274, 356804, 671224, 1269022, 2404289, 4521836, 8535117, 16134474, 30635869, 58062404, 110496946, 210500898, 401422210, 767158570, 1467402238 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..2000 EXAMPLE a(6) = 3: 2 + 3 + 5 - 7 + 11 - 13 = -2 + 3 + 5 - 7 - 11 + 13 = -2 + 3 - 5 + 7 + 11 - 13 = 1. MAPLE s:= proc(n) s(n):= `if`(n<1, 0, ithprime(n)+s(n-1)) end: b:= proc(n, i) option remember; `if`(n>s(i), 0, `if`(i=0, 1, b(n+ithprime(i), i-1)+b(abs(n-ithprime(i)), i-1))) end: a:=n-> b(0, n)+b(1, n): seq(a(n), n=0..45); # Alois P. Heinz, Jan 16 2022 MATHEMATICA s[n_] := s[n] = If[n < 1, 0, Prime[n] + s[n - 1]]; b[n_, i_] := b[n, i] = If[n > s[i], 0, If[i == 0, 1, b[n + Prime[i], i - 1] + b[Abs[n - Prime[i]], i - 1]]]; a[n_] := b[0, n] + b[1, n]; Table[a[n], {n, 0, 45}] (* Jean-François Alcover, Mar 01 2022, after Alois P. Heinz *) PROG (Python) from itertools import product from sympy import prime, primerange def a(n): if n == 0: return 1 nn = ["0"] + [str(i) for i in primerange(2, prime(n)+1)] return sum(eval("".join([*sum(zip(nn, ops+("", )), ())])) in {0, 1} for ops in product("+-", repeat=n)) print([a(n) for n in range(18)]) # Michael S. Branicky, Jan 16 2022 (Python) from sympy import sieve, primerange from functools import cache @cache def b(n, i): maxsum = 0 if i == 0 else sum(p for p in primerange(2, sieve[i]+1)) if n > maxsum: return 0 if i == 0: return 1 return b(n+sieve[i], i-1) + b(abs(n-sieve[i]), i-1) def a(n): return b(0, n) + b(1, n) print([a(n) for n in range(43)]) # Michael S. Branicky, Jan 16 2022 CROSSREFS Cf. A000040, A022894, A025591, A113040. Sequence in context: A290973 A173497 A022875 * A325841 A076480 A002730 Adjacent sequences: A350401 A350402 A350403 * A350405 A350406 A350407 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Dec 29 2021 EXTENSIONS a(39)-a(40) from Michael S. Branicky, Jan 16 2022 STATUS approved

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Last modified May 22 04:07 EDT 2024. Contains 372742 sequences. (Running on oeis4.)