

A064653


Integers not expressible as p + q*a^2, a>1 and p, q are primes.


2



1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 16, 18, 24, 26, 28, 36, 42, 60, 72, 84, 90, 96, 108, 240, 300, 420, 1050, 1260
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OFFSET

1,2


COMMENTS

Dean Hickerson (Oct 12 2001) writes: I suspect that there are no more terms in the sequence. In fact, I'll make the stronger conjecture that for all n>1260, n can be written as p + q*a^2 where a is the smallest prime that does not divide n. For example, for n=10080, a=11 and we have the representation 10080 = 7297 + 23 * 11^2.
There are no other terms up to 10^7.
Hickerson's stronger conjecture holds for n <= 10^9. Therefore, there are no other terms up to 10^9.  David A. Corneth, Jun 17 2019


LINKS

Table of n, a(n) for n=1..28.


EXAMPLE

18 is in the sequence because p + 2*2^2 would imply that p is 10, or p + 2*3^2 would imply that p is 0, or p+ 3*2^2 would imply that p is 6, all of which are composite numbers.


MATHEMATICA

Complement[Range[2000], Union@Flatten@Outer[Plus, Prime[Range[PrimePi[2000]]], Union@Flatten@Outer[Times, Prime[Range[PrimePi[2000]]], Table[a^2, {a, 2, 20}]]]] (* Robert Price, Jun 16 2019 *)


CROSSREFS

A subsequence of A064915.
Sequence in context: A048381 A185186 A115569 * A130588 A079238 A079042
Adjacent sequences: A064650 A064651 A064652 * A064654 A064655 A064656


KEYWORD

nonn,more


AUTHOR

Robert G. Wilson v, Oct 07 2001


EXTENSIONS

Two more terms from Dean Hickerson, Oct 12 2001


STATUS

approved



