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A236128
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Primes p such that gpf(gpf(2^p-1)-1) = p.
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2
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OFFSET
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1,1
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COMMENTS
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No more terms found up to p = 1277, 1277 being the first prime for which the complete factorization of 2^p-1 is not currently known (see GIMPS link). - Michel Marcus, Jan 20 2014
Conjecture: gpf(gpf(2^p-1)-1) = p for finitely many p.
Conjecture: gpf(lpf(2^p-1)-1) = p for infinitely many p.
Namely, for p = 2, 3, 5, 7, 11, 13, 23, 29, 37, 43, 47, 53, ... - Michael B. Porter, Jan 26 2014
Note that gpf(lpf(2^p-1)-1) = gpf(gpf(2^p-1)-1) = p for p = 2, 3, 5, 7, 11, 13, 29, 53. See DATA.
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LINKS
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EXAMPLE
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For prime p=2, 2^p-1=3, gpf(3)=3, gpf(3-1)=2, so 2 is in the sequence.
For prime p=3, 2^p-1=7, gpf(7)=7, gpf(7-1)=3, so 3 is in the sequence.
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MATHEMATICA
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Select[Prime[Range[25]], FactorInteger[FactorInteger[2^# - 1][[-1, 1]] - 1][[-1, 1]] == # &] (* Alonso del Arte, Jan 19 2014 *)
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PROG
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(PARI) isok(p) = isprime(p) && (q = (vecmax(factor(2^p-1)[, 1]))) && (vecmax(factor(q-1)[, 1]) == p); \\ Michel Marcus, Jan 19 2014
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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