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Search: id:A083955
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| A083955 |
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Numbers n > 1 such that n^5 - 2 has no prime factor > n. |
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+0
7
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| 3557, 12038, 14810, 15424, 28456, 30742, 31540, 37665, 45602, 46883, 47879, 48152, 52196, 52617, 55265, 57902, 68306, 69032, 74925, 76262, 79562, 79984, 84569, 90442, 104867, 104956, 107213, 112570, 114614, 119477, 127634, 131072, 132466
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also integers n > 1 for which there is no prime p > n such that x = n is a solution mod p of x^5 = 2, since the following equivalences hold for n > 1: There is a prime p > n such that n is a solution mod p of x^5 = 2 iff n^5 - 2 has a prime factor > n; n is a solution mod p of x^5 = 2 iff p is a prime factor of n^5 - 2 and p > n.
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EXAMPLE
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12038 is a term since 12038^5 - 2 = 252796871460867395166 = 2*3*3*3*263*571*641*911*5849*9127 has no prime factor > 12038.
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PROGRAM
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(PARI) {for(n=2, 133000, f=factor(n^5-2); if(f[matsize(f)[1], 1]<=n, print1(n, ", ")))}
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CROSSREFS
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Cf. A040159, A040160, A065903.
Sequence in context: A035779 A108003 A020412 this_sequence A104207 A107646 A071144
Adjacent sequences: A083952 A083953 A083954 this_sequence A083956 A083957 A083958
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 09 2003
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