A358867 Primes from which subtracting the sum of the first k primes does not yield another prime, for any k.

2, 3, 11, 37, 67, 97, 127, 157, 211, 223, 277, 307, 337, 367, 373, 379, 397, 409, 439, 727, 739, 769, 853, 937, 967, 991, 1069, 1129, 1171, 1399, 1447, 1567, 1579, 1597, 1693, 1753, 1777, 1783, 1831, 1861, 1987, 2203, 2617, 3067, 3109, 3793, 4561, 4603, 4783, 4993, 5323, 5431, 5557, 6211, 6373, 7741

Offset

1,1

Comments

The greater prime p of a twin prime pair is never a term, since p-2 is the lesser prime of that pair. Terms of A013918 are not terms here either because at the (k-1)-th subtraction the result is the k-th prime.

Given comments in A090304, the last term is likely a(56) = 7741. - Michael S. Branicky, Dec 03 2022

Links

Table of n, a(n) for n=1..56.

Example

11 is a term because 11 - 2 = 9, 11 - (2 + 3) = 6, 11 - (2 + 3 + 5) = 1, and none of these are prime.
17 is not a term because 17 - (2 + 3 + 5) = 7, which is prime.

Mathematica

primeQ[n_] := n > 0 && PrimeQ[n]; With[{p = Prime[Range[1000]]}, s = Accumulate[p]; q[n_] := AllTrue[s, ! primeQ[n - #] &]; Select[p, q]] (* Amiram Eldar, Dec 04 2022 *)

Crossrefs

Primes in A090304.

Cf. A000040, A007504.

Sequence in context: A019361 A093804 A084121 * A088747 A231574 A365288

Adjacent sequences: A358864 A358865 A358866 * A358868 A358869 A358870

Keyword

nonn

Author

Tamas Sandor Nagy, Dec 03 2022

Extensions

More terms from Michael S. Branicky, Dec 03 2022

Status

approved