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A064653
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Integers not expressible as p + q*a^2, a>1 and p, q are primes.
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2
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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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listen;
history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..28.
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EXAMPLE
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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.
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CROSSREFS
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A subsequence of A064915.
Sequence in context: A048381 A185186 A115569 * A130588 A079238 A079042
Adjacent sequences: A064650 A064651 A064652 * A064654 A064655 A064656
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v, Oct 07 2001
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EXTENSIONS
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Two more terms from Dean Hickerson, Oct 12, 2001
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STATUS
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approved
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