A344581 Numbers k such that A034387(k) and A101203(k) are both prime.

4, 7, 8, 15, 44, 311, 503, 507, 744, 843, 851, 955, 1164, 1256, 1287, 1307, 1312, 2163, 2171, 2244, 2247, 2368, 2412, 3143, 3160, 3872, 3875, 3952, 4584, 5088, 5236, 5355, 5364, 5380, 6211, 6303, 6307, 6587, 7243, 7244, 7436, 7439, 7860, 8220, 8268, 9167, 9283, 9515, 9519, 9632, 9692, 9915, 9919

Offset

1,1

Comments

Numbers k such that the sums of primes <= k and of nonprimes <= k are both prime (not necessarily distinct).

All terms == 0 or 3 (mod 4).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 8 is a term because A034387(8) = 2+3+5+7 = 17 and A101203(8) = 1+4+6+8 = 19 are prime.

Maple

sp:= proc(n) option remember; if isprime(n) then procname(n-1)+[0, n] else procname(n-1)+[n, 0] fi end proc:
sp(1):= [1, 0]:
filter:= proc(n) andmap(isprime, sp(n)) end proc:
select(filter, [$1..10000]);

Crossrefs

Cf. A034387, A101203. Intersection of A228102 and A344580.

Sequence in context: A324854 A086987 A051219 * A270216 A237599 A291750

Adjacent sequences: A344578 A344579 A344580 * A344582 A344583 A344584

Keyword

nonn

Author

J. M. Bergot and Robert Israel, May 24 2021

Status

approved