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Search: id:A132657
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| A132657 |
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Smallest prime between n^2 and (n+1)^2 times largest prime between n^2 and (n+1)^2. |
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1
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| 6, 35, 143, 391, 899, 1739, 3233, 5293, 8051, 11413, 17653, 24883, 33389, 43931, 56977, 72731, 92881, 118829, 145699, 176039, 212197, 254701, 308911, 357163, 424663, 492179, 566609, 660293, 756611, 864371, 987307, 1120697, 1257923
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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First 5 values are a subset of A132435. Subset of semiprimes A001358. Suggested by Legendre's conjecture (still open) that there is always a prime between n^2 and (n+1)^2. A053001(n+1) - A007491(n) = 1, 2, 2, 6, 2, 10, 8, 12, 14, 12, 12, 18, 20, 26, 24, 26, 24, 28, 30, 38, ... not currently in OEIS.
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FORMULA
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a(n) = A007491(n) * A053001(n+1).
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EXAMPLE
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a(1) = 6 = 2*3 = (smallest prime in [1^2,2^2]) * (largest prime in [1^2,2^2]).
a(2) = 35 = 5*7 = (smallest prime in [2^2,3^2]) * (largest prime in [2^2,3^2]).
a(3) = 143 = 11*13 = (smallest prime in [2^2,3^2]) * (largest prime in [2^2,3^2]).
a(4) = 391 = 17*23 = (smallest prime in [3^2,4^2]) * (largest prime in [3^2,4^2]).
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MATHEMATICA
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Table[Prime[PrimePi[n^2] + 1]*Prime[PrimePi[(n + 1)^2]], {n, 1, 40}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 20 2007
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CROSSREFS
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Cf. A000040, A001358, A007491, A014085, A053000, A053001, A053607, A077766, A077767, A132435.
Sequence in context: A094952 A024526 A089581 this_sequence A027985 A078799 A026957
Adjacent sequences: A132654 A132655 A132656 this_sequence A132658 A132659 A132660
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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), Nov 15 2007
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 20 2007
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