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Search: id:A115948
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| A115948 |
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a(n) = (2^(semiprime(n)-1)) modulo (semiprime(n)^2). |
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+0
1
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| 8, 32, 13, 12, 156, 184, 319, 464, 341, 496, 301, 308, 9, 952, 472, 508, 1191, 922, 2359, 688, 1800, 2668, 2291, 3109, 2888, 4860, 412, 4691, 604, 2875, 4523, 2236, 3856, 5659, 2016, 8662, 3259, 8852, 13239, 6953, 1344, 6277, 7357, 2857, 11660, 18193
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Wieferich function of semiprimes.
This appears in the search for the semiprime analogy to A001220 Wieferich primes p: p^2 divides 2^(p-1) - 1. That is, the Wieferich function W(p) of primes p is W(p) = 2^(p-1) modulo p^2 and a (rare!) Wieferich prime (A001220) is one such that W(p) = 1. The current sequence is W(semiprime(n)). Any semiprime s for which W(s) = 1 would be a "Wieferich semiprime." This is also related to Fermat's "little theorem" that for any odd prime p we have 2^(p-1) == 1 modulo p.
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REFERENCES
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R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 28.
R. K. Guy, Unsolved Problems in Number Theory, A3.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 91.
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FORMULA
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a(n) = (2^(A001358(n)-1)) modulo (A001358(n)^2).
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MATHEMATICA
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PowerMod[2, # - 1, #^2] & /@ Select[ Range@141, Plus @@ Last /@ FactorInteger@# == 2 &] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A001220, A001358.
Sequence in context: A121097 A121093 A102275 this_sequence A059880 A144096 A127988
Adjacent sequences: A115945 A115946 A115947 this_sequence A115949 A115950 A115951
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 14 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Mar 14 2006
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