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

Author

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

Keywords

• nonn

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).

Examples

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

Links

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

Crossrefs

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

Programs

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]);