

A309264


Numbers k such that s + t = k with 0 < s < t where t and ts are both prime.


1



4, 7, 8, 9, 11, 12, 15, 17, 19, 20, 21, 23, 24, 25, 27, 29, 31, 32, 33, 35, 36, 39, 41, 43, 44, 45, 47, 49, 51, 53, 55, 56, 57, 59, 60, 61, 63, 65, 67, 69, 71, 72, 73, 75, 77, 79, 80, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 99, 101, 103, 104, 105, 107
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..64.


EXAMPLE

4 is in the sequence since there are numbers, s=1 and t=3, that satisfy s + t = 4, where s < t, t = 3 (prime) and ts = 31 = 2 (prime).
7 is in the sequence since there are numbers, s=2 and t=5 that satisfy s + t = 7, where s < t, t = 5 (prime) and ts = 52 = 3 (prime).


MATHEMATICA

Flatten[Table[If[Sum[(PrimePi[n  i]  PrimePi[n  i  1]) (PrimePi[n  2 i]  PrimePi[n  2 i  1]), {i, Floor[n/2]}] > 0, n, {}], {n, 100}]]


PROG

(PARI) isok(k) = {forprime (t=1, k, if (((s = k  t) < t) && (s > 0) && isprime(ts), return (1)); ); } \\ Michel Marcus, Jul 20 2019


CROSSREFS

Cf. A309152, A309265.
Sequence in context: A004710 A060257 A262874 * A161986 A324940 A020670
Adjacent sequences: A309261 A309262 A309263 * A309265 A309266 A309267


KEYWORD

nonn


AUTHOR

Wesley Ivan Hurt, Jul 19 2019


STATUS

approved



