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Search: id:A124110
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| A124110 |
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Primes of the form A124080 (10 times triangular numbers) +- 1. |
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+0
3
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| 11, 29, 31, 59, 61, 101, 149, 151, 211, 281, 359, 449, 659, 661, 911, 1049, 1051, 1201, 1361, 1531, 1709, 1901, 2099, 2309, 2311, 2531, 2999, 3001, 3251, 3511, 3779, 4349, 4649, 4651, 5279, 5281, 6299, 6301, 6659, 6661, 7411, 8609, 9029, 9461, 9901, 11279
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Numbers j such that A124080(j)-1 is prime or A124080(j)+1 is prime, where repetition means a twin prime, are 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8, 9, 11, 11, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 21, 22, 24, 24, 25, ..., . - Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 29 2006
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FORMULA
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{A124080(j)-1 when prime} U {A124080(j)+1 when prime} = {i = 10*T(j)-1 such that i is prime} U {i = 10*T(j)+1 such that i is prime} where T(j) = A000217(j) = j*(j+1)/2.
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EXAMPLE
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a(1) = A124080(1)+1 = (10*T(1)) - 1 = 10*(1*(1+1)/2) + 1 = 10+1 = 11 is prime.
a(2) = A124080(2)-1 = (10*T(2))-1 = 10*(2*(2+1)/2) - 1 = 30-1 = 29 is prime.
a(3) = A124080(2)+1 = (10*T(2))+1 = 10*(2*(2+1)/2) + 1 = 30+1 = 31 is prime.
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MATHEMATICA
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s = {}; Do[t = 5n(n + 1); If[PrimeQ[t - 1], AppendTo[s, t - 1]]; If[PrimeQ[t + 1], AppendTo[s, t + 1]], {n, 47}]; s (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000040, A000217, A028895, A046092, A045943, A002378, A028896, A024966, A033996, A027468.
Sequence in context: A005110 A059337 A126240 this_sequence A153768 A092194 A134307
Adjacent sequences: A124107 A124108 A124109 this_sequence A124111 A124112 A124113
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 26 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 29 2006
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