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A125773
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Numbers n that are not the powers of 2 such that 2^n (mod n) = 2^n (mod n^2); or A068535(n) with powers of 2 excluded.
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2
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35, 297, 1093, 2186, 2590, 3279, 3511, 4372, 5465, 6558, 7022, 7651, 8744, 9837, 10533, 10930, 13116, 14044, 14209, 21066, 23175, 24012, 24577, 26592, 28088, 31599, 35110, 38621, 42132, 49154, 987704, 3020871, 3074592
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A068535(n) includes all powers of 2. a(3) = 1093 and a(7) = 3511 are the only known primes in a(n). They belong to A001220(n) = Wieferich primes p: p^2 divides 2^(p-1) - 1. Note that most listed terms of a(n) are the multiples of Wieferich primes 1093 and 3511. No more terms in a(n) up to 6*10^6.
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MATHEMATICA
| Do[f=PowerMod[2, n, n]; g=PowerMod[2, n, n^2]; If[f==g&&!IntegerQ[Log[2, n]], Print[n]], {n, 1, 6000000}]
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CROSSREFS
| Cf. A068535 = numbers n such that 2^n (mod n) = 2^n (mod n^2). Cf. A001220 = Wieferich primes p: p^2 divides 2^(p-1) - 1. Cf. A125774 = numbers n such that 3^n (mod n) = 3^n (mod n^2). Cf. A125775 = numbers n such that 5^n (mod n) = 5^n (mod n^2).
Sequence in context: A145014 A090646 A055658 * A198397 A071697 A027792
Adjacent sequences: A125770 A125771 A125772 * A125774 A125775 A125776
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 07 2006
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