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A360930
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Odd numbers which cannot be expressed as p + q*(q-1) where p and q are primes.
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2
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1, 3, 41, 97, 135, 251, 255, 341, 363, 377, 405, 671, 737, 765, 1007, 1049, 1287, 1371, 1377, 1427, 1605, 1697, 1745, 1805, 2067, 2177, 2201, 2277, 2333, 2477, 2657, 2711, 3077, 3101, 3117, 3149, 3191, 3437, 3557, 3597, 3611, 3983, 4647, 4787, 4797, 5117
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OFFSET
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1,2
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COMMENTS
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It is conjectured that 772277 is the largest odd integer which cannot be expressed as p + q*(q-1) where p and q are primes.
q*(q-1) is even which implies that p must be an odd prime.
The expression p + q*(q-1) resembles the expression p + 2*q used in Lemoine's conjecture.
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LINKS
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MATHEMATICA
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a[1]=1; a[n_]:=a[n]=(k=a[n-1]; c=True; While[c, k=k+2; c=False; q=2; While[!c&&q*(q-1)<k, p=k-(q*(q-1)); c=PrimeQ[p]; q=NextPrime[q]]]; k); Table[a[n], {n, 1, 150}]
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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