

A306394


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


1



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
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OFFSET

1,2


COMMENTS

Contains 36*k^2 unless 6*k1 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), 335363.


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..(Nj)/6), j=[0, 2])} minus PP2, list));


CROSSREFS

Cf. A005384, A109136.
Sequence in context: A117612 A320662 A171613 * A109136 A295522 A065131
Adjacent sequences: A306391 A306392 A306393 * A306395 A306396 A306397


KEYWORD

nonn


AUTHOR

Robert Israel, Feb 12 2019


STATUS

approved



