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A358867
Primes from which subtracting the sum of the first k primes does not yield another prime, for any k.
0
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
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.
Sequence in context: A019361 A093804 A084121 * A088747 A231574 A365288
KEYWORD
nonn
AUTHOR
Tamas Sandor Nagy, Dec 03 2022
EXTENSIONS
More terms from Michael S. Branicky, Dec 03 2022
STATUS
approved