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A023506
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Exponent of 2 in prime factorization of prime(n) - 1.
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15
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0, 1, 2, 1, 1, 2, 4, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 3, 5, 2, 1, 1, 2, 4, 1, 1, 3, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 6, 2, 1, 1, 1, 1, 2, 3, 1, 4, 1, 8, 1, 2, 1, 2, 3, 1, 2, 1, 1, 3, 2, 1, 4, 1, 2, 5, 1, 1, 2, 1, 1, 2, 2, 4, 3, 1, 2, 1, 4, 1, 1, 6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 2, 1, 2, 1, 3, 1
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OFFSET
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1,3
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COMMENTS
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Also the number of steps to reach an integer starting with prime(n)/2 and iterating the map x->x*ceiling(x). - Benoit Cloitre, Sep 06 2002
Also exponent of 2 in -1 + prime(n)^s for odd exponents s because (-1 + prime(n)^s)/(prime(n) - 1) is odd. - Labos Elemer, Jan 20 2004
First occurrence of 0,1,2,3,4,...: 1, 2, 3, 13, 7, 25, 44, 116, 55, 974, 1581, 2111, 1470, 4289, 10847, 15000, 6543, 91466, 62947, 397907, 498178, ..., for primes 2, 3, 5, 41, 17, 97, 193, 641, 257, 7681, 13313, 18433, 12289, 40961, 114689, 163841, 65537, 1179649, 786433, 5767169, 7340033, .... - Robert G. Wilson v, May 28 2009
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LINKS
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FORMULA
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EXAMPLE
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n=25, p(25)=97, A006093(25) = 96 = 2*2*2*2*2*3, so a(25)=5.
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MAPLE
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A023506:= x -> padic[ordp](ithprime(x)-1, 2):
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MATHEMATICA
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f[n_] := Block[{fi = First@ FactorInteger[ Prime@n - 1]}, If[ fi[[1]] == 2, fi[[2]], 0]]; Array[f, 105] (* Robert G. Wilson v, May 28 2009 *)
Table[IntegerExponent[Prime[n] - 1, 2], {n, 110}] (* Bruno Berselli, Aug 05 2013 *)
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PROG
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(PARI) forprime(p=2, 700, print1(valuation(p-1, 2), ", ")); \\ Bruno Berselli, Aug 05 2013
(Magma) [Valuation(NthPrime(n)-1, 2): n in [1..110]]; // Bruno Berselli, Aug 05 2013
(Python)
from sympy import prime
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CROSSREFS
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Subsequence of A001511 (except 1st term).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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