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Search: id:A122211
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| A122211 |
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Numbers n such that the sum of squares of the first n^2 primes is a prime. |
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3
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| 6, 12, 30, 66, 156, 180, 228, 336, 366, 558, 750, 840, 894, 978, 1398, 1410, 1506, 1560, 1578, 1662, 1794, 1800, 1812, 1824, 1890, 1992, 2094, 2268, 2334, 2358, 2430, 2604, 2736, 2742
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) are the primes in A122209[n] = {4,87,1556,13275,65796,239087,710844,1789395,...}. Corresponding primes A122209[ a(n) ] = A024450[ a(n)^2 ] are listed in A122210[n] = {239087,29194283,13459558559,2330212120559,...}. It appears that all a(n) are of the form 6k, where k = {1,2,5,11,26,30,38,56,61,93,125,140,149,163,233,235,251,260,263,277,299,300, 302,304,315,332,349,378,389,393,405,434,456,457,...}.
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FORMULA
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A122209[ a(n) ] = A024450[ a(n)^2 ] = A122210[n].
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MATHEMATICA
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s=0; Do[p=Prime[n]; k=Sqrt[n]; s=s+p*p; If[PrimeQ[s]&&IntegerQ[k], Print[{k, n, s}]], {n, 1, 10^7}]
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CROSSREFS
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Cf. A122209, A122210, A024450, A098561, A098562.
Sequence in context: A011987 A036690 A014131 this_sequence A015801 A073245 A119626
Adjacent sequences: A122208 A122209 A122210 this_sequence A122212 A122213 A122214
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 26 2006
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