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Search: id:A121926
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| 3, 5, 11, 31, 131, 733, 5057, 40339, 362903, 3628829, 39916831, 479001637, 6227020841, 87178291243, 1307674368047, 20922789888053, 355687428096059, 6402373705728061, 121645100408832067, 2432902008176640071, 51090942171709440073, 1124000727777607680079
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OFFSET
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1,1
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COMMENT
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It was conjectured by Alexander R. Povolotsky and proved (in SeqFan email exchange) by David Harden (with proof improvement from Daniel Berend) that no value of n exists such that ( n! + prime(n) ) yields integral square. Alexander R. Povolotsky also conjectured (no proof yet) that no value of n exists such that ( n! + prime(n) ) yields integral m^k where k>1 [From Alexander R. Povolotsky (pevnev(AT)juno.com), Aug 13 2008]
The sum of reciprocals of this sequence's terms converges to: PARI suminf(n=1, 1/(prime(n) + n!)) = 0.6657239270705138461513344444 [From Alexander R. Povolotsky (pevnev(AT)juno.com), Sep 22 2008]
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CROSSREFS
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Sequence in context: A095184 A048235 A154939 this_sequence A063499 A082856 A060881
Adjacent sequences: A121923 A121924 A121925 this_sequence A121927 A121928 A121929
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Aug 13 2008
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