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Search: id:A125771
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| A125771 |
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Primes of the form j*T_k +/- 1, where T_k is the k-th triangular number greater than 9. |
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+0
2
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| 11, 19, 29, 31, 37, 41, 43, 59, 61, 67, 71, 73, 79, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 167, 179, 181, 191, 197, 199, 211, 223, 229, 233, 239, 241, 251, 263, 269, 271, 277, 281, 293, 307, 311, 313, 331, 337, 349, 359, 379, 389, 397
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Since all primes would eventually appear in A125765 or A125766 because (p +/-1) times 1(1+1)/2 equals (p +/- 1) let us not use the first triangular number 1.
Primes not of the form j*T_k +/- 1, where T_k is the k-th triangular number greater than 1 only produces one prime: 3. If we restrict triangular numbers greater than 5, then only two primes are found: 2 & 3.
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EXAMPLE
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11 = 1*10 +1,
19 = 2*10 -1, etc.
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MATHEMATICA
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s = {}; Do[m = j*k*(k + 1)/2; If[ PrimeQ[m - 1], AppendTo[s, m - 1]]; If[ PrimeQ[m + 1], AppendTo[s, m + 1]], {j, 40}, {k, 4, 23}]; Take[ Union@s, 75]
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CROSSREFS
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Cf. A000217, A125765, A125766, A125767, A125768, A125769, A125770.
Sequence in context: A129916 A032694 A004769 this_sequence A158290 A057538 A123976
Adjacent sequences: A125768 A125769 A125770 this_sequence A125772 A125773 A125774
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com) & Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 05 2006
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