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Search: id:A146968
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| A146968 |
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Natural numbers n with property that n!+1=p^2 where, if p is a natural number, it's a prime. I tested it from 1 to 7530 and it wonderfully seems that n!+1=p^2 produces only primes... However, until 7530, the only 3 numbers that makes p a natural number are 4, 5 and 7 (and they produce 3 primes). I submit it hoping that somebody can find other numbers or finally convince me it's only a soap bubble (or something known). |
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+0
2
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OFFSET
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1,1
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COMMENT
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No other terms up to 8047. The MAGMA program below generates the pairs <n, p>: <4, 5>, <5, 11>, <7, 71>. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 05 2008]
Used the PARI script below to check new terms up to 60100. No new terms were found. [From Marco Bellaccini (marcomurk(AT)tele2.it), Nov 08 2008]
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EXAMPLE
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7! + 1 = 5041 = 71^2, hence 7 is in the sequence. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 05 2008]
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PROGRAM
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(Shell) #!/bin/sh n=0 while(true) do n=`echo $n + 1 | bc` calc "($n! + 1)" ^ "(1 / 2)" | grep -v \. done
(MAGMA) [ <n, p>: n in [1..8047] | t where t, p:=IsSquare(Factorial(n)+1) ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 05 2008]
(PARI) { for (n=1, 60100, if(issquare(n!+1) == 1, print(n) ) ) } [From Marco Bellaccini (marcomurk(AT)tele2.it), Nov 08 2008]
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CROSSREFS
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Sequence in context: A019067 A095212 A166042 this_sequence A112247 A057055 A114343
Adjacent sequences: A146965 A146966 A146967 this_sequence A146969 A146970 A146971
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KEYWORD
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bref,more,nonn
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AUTHOR
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Marco Bellaccini (marcomurk(AT)tele2.it), Nov 03 2008
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