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Search: id:A023186
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| A023186 |
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Lonely (or isolated) primes: increasing distance to nearest prime. |
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+0
21
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| 2, 5, 23, 53, 211, 1847, 2179, 3967, 16033, 24281, 38501, 58831, 203713, 206699, 413353, 1272749, 2198981, 5102953, 10938023, 12623189, 72546283, 142414669, 162821917, 163710121, 325737821, 1131241763, 1791752797, 3173306951, 4841337887, 6021542119, 6807940367, 7174208683, 8835528511, 11179888193, 15318488291, 26329105043, 31587561361, 45241670743
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Erdos and Suranyi call these reclusive primes and prove that there are an infinite number of them. They define these primes to be between two primes. Hence their first term would be 3 instead of 2. Record values in A120937. - T. D. Noe (noe(AT)sspectra.com), Jul 21 2006
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REFERENCES
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Paul Erdos and Janos Suranyi, Topics in the theory of numbers, Springer, 2003.
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EXAMPLE
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The nearest prime to 23 is 4 units away, larger than any previous prime, so 23 is in the sequence.
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MATHEMATICA
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 0; q = 2; i = 0; Do[r = NextPrim[q]; m = Min[r - q, q - p]; If[m > i, Print[q]; i = m]; p = q; q = r, {n, 1, 152382000}]
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CROSSREFS
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Related sequences: A023186-A023188, A046929-A046931, A051650, A051652, A051697-A051702, A051728-A051730.
The distances are in A023187.
Sequence in context: A141181 A100031 A126975 this_sequence A023188 A106858 A100299
Adjacent sequences: A023183 A023184 A023185 this_sequence A023187 A023188 A023189
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KEYWORD
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nonn,nice
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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More terms from Jud McCranie (j.mccranie(AT)comcast.net), Jun 16 2000
More terms from T. D. Noe (noe(AT)sspectra.com), Jul 21 2006
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