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A344581 Numbers k such that A034387(k) and A101203(k) are both prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 26 07:15 EST 2022. Contains 350573 sequences. (Running on oeis4.)