A306394 Numbers k == 0 or 2 (mod 6) which are not the sum of a prime and the square of a prime.

0, 2, 8, 18, 24, 74, 170, 324, 614, 704, 1010, 1164, 1296, 2304, 3600, 4356, 5184, 6084, 9216, 10404, 11664, 14400, 15054, 15876, 19044, 20736, 21774, 22500, 24336, 24476, 26244, 28224, 34596, 39204, 41616, 44100, 46656, 49284, 51984, 60516, 66564, 69696, 72900, 76176, 82944, 90000, 93636, 97344

Offset

1,2

Comments

Contains 36*k^2 unless 6*k-1 is in A005384.

Are 2, 8, 18, 24, 74, 170, 614, 704, 1010, 1164, 15054, 21774, 24476 the only terms not == 0 or 36 (mod 144)?

Links

Robert Israel, Table of n, a(n) for n = 1..652

A. V. Kumchev and J. Y. Liu, Sums of primes and squares of primes in short intervals, Monatsh. Math. 157 (2009), 335-363.

Example

24 is in the sequence because 24 == 0 (mod 6) and 24 can't be written as p+q^2 where p and q are primes.

Maple

N:= 50000: # to get all terms <= N
P:= select(isprime, [2, seq(i, i=3..N, 2)]):
P2:= select(`<=`, map(`^`, P, 2), N):
PP2:= {seq(seq(s+t, s=P), t=P2)}:
sort(convert({seq(seq(6*i+j, i=1=0..(N-j)/6), j=[0, 2])} minus PP2, list));

Crossrefs

Cf. A005384, A109136.

Sequence in context: A320662 A171613 A338140 * A109136 A295522 A065131

Adjacent sequences: A306391 A306392 A306393 * A306395 A306396 A306397

Keyword

nonn

Author

Robert Israel, Feb 12 2019

Status

approved