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Search: id:A129634
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| A129634 |
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Least nonnegative m such that T(n) + T(m) is prime, where T(n) = n(n+1)/2. |
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2
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| 2, 1, 0, 1, 1, 7, 4, 1, 1, 7, 3, 1, 1, 3, 16, 13, 1, 4, 4, 1, 1, 4, 4, 1, 46, 3, 7, 1, 2, 7, 16, 2, 13, 4, 3, 1, 13, 3, 4, 22, 1, 16, 16, 1, 1, 7, 3, 1, 10, 3, 7, 1, 2, 7, 16, 2, 1, 4, 4, 13, 1, 4, 16, 1, 1, 16, 4, 2, 1, 16, 8, 1, 10, 3, 7, 1, 1, 31, 7, 2, 13, 4, 4, 10, 1, 8, 7, 13, 1, 43, 16, 5, 25, 16
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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What is the simplest proof that this is defined for all nonzero n?
It appears that a(n)<n except for n=0,5,14,24. The graph of A130504 provides evidence that a(n) exists for all n. - T. D. Noe (noe(AT)sspectra.com), Jun 04 2007
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
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FORMULA
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a(n) = Min{m: m*(m+1)/2 + n*(n+1)/2 is prime}. a(n) = Min{m: A000217(m) + A000217(n) is an element of A000040}.
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EXAMPLE
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a(6) = 4 because T(4) = 10 is the least triangular number whose sum with T(6) = 21 is prime, since {21+0 = 3*7, 21+3 = 2^3*3, 21+6 = 3^3} are all composite, but 21+10 = 31 is prime.
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MATHEMATICA
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nn=100; tri=Range[0, nn]Range[nn+1]/2; Table[k=1; While[k<=Length[tri] && !PrimeQ[tri[[k]]+tri[[n]]], k++ ]; If[k<=Length[tri], k-1, 0], {n, Length[tri]}] - T. D. Noe (noe(AT)sspectra.com), Jun 04 2007
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CROSSREFS
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Cf. A000040, A000217, A129755, A130334.
Cf. A069003 (for square numbers).
Sequence in context: A103631 A083856 A081718 this_sequence A066438 A051126 A063933
Adjacent sequences: A129631 A129632 A129633 this_sequence A129635 A129636 A129637
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), May 31 2007
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EXTENSIONS
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Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Jun 04 2007
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