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Search: id:A123599
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| A123599 |
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Smallest generalized Fermat prime of the form a^(2^n) + 1, where base a>1 is an integer; or -1 if no such prime exists. |
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+0
4
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| 3, 5, 17, 257, 65537, 185302018885184100000000000000000000000000000001, 35514932432768748051296033480782041744270341164974614340815819747860363630206671\ 9166373229531510062746472251495292613758147362817, 13652101047499351886612295337097017212495117378851463216706986355793509781866641\ 16487286492188065715081609508117276650596643981892041834496000000000000000000000\ 00000000000000000000000000000000000000000000000000000000000000000000000000000000\ 000000000000000000000000001
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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First 5 terms {3, 5, 17, 257, 65537} = A019434(n) are the Fermat primes of the form 2^(2^n) + 1. Note that for all currently known a(n) up to n = 17 last digit is 7 or 1 (except a(0) = 3 and a(1) = 5). Corresponding least bases a>1 such that a^(2^n) + 1 is prime are listed in A056993(n) = {2, 2, 2, 2, 2, 30, 102, 120, 278, 46, 824, 150, 1534, 30406, 67234, 70906, 48594, 62722, ...}.
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LINKS
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Eric Weisstein's World of Mathematics, Generalized Fermat Number.
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MATHEMATICA
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Do[f=Min[Select[ Table[ i^(2^n) + 1, {i, 2, 500} ], PrimeQ]]; Print[{n, f}], {n, 0, 9}]
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CROSSREFS
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Cf. A019434 = Fermat primes of the form 2^(2^n) + 1. Cf. A000215 = Fermat numbers: 2^(2^n) + 1. Cf. A056993 = smallest k >= 2 such that k^(2^n)+1 is prime. Cf. A006093, A005574, A000068, A006314, A006313, A006315, A006316, A056994, A056995, A057465, A057002.
Sequence in context: A050922 A070592 A000215 this_sequence A100270 A016045 A128336
Adjacent sequences: A123596 A123597 A123598 this_sequence A123600 A123601 A123602
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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), Nov 14 2006
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