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 A291691 Primes p such that gpf(lpf(2^p - 1) - 1) = p. 3
 2, 3, 5, 7, 11, 13, 23, 29, 37, 43, 47, 53, 73, 79, 83, 97, 113, 131, 151, 173, 179, 181, 191, 197, 211, 223, 233, 239, 251, 263, 277, 281, 283, 307, 317, 337, 353, 359, 367, 383, 397, 419, 431, 439, 443, 457, 461, 463, 467, 487, 491, 499 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence has not been proved to be infinite. The terms p such that 2^p - 1 is a Mersenne prime are 2, 3, 5, 7, and 13. If p is prime, then gpf(lpf(2^p - 1) - 1) >= p. Primes q such that gpf(lpf(2^q - 1) - 1) > q are A292237. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..119 EXAMPLE We have gpf(lpf(2^11 - 1) - 1) = gpf(23 - 1) = 11, so 11 is a term. MATHEMATICA lpf[n_] := FactorInteger[n][[1, 1]]; gpf[n_] := FactorInteger[n][[-1, 1]]; Select[ Prime@ Range@ 45, gpf[lpf[2^# - 1] - 1] == # &] (* Giovanni Resta, Aug 30 2017 *) PROG (PARI) listp(nn) = forprime(p=2, nn, if (vecmax(factor(vecmin(factor(2^p-1)[, 1])-1)[, 1]) == p, print1(p, ", ")); ); \\ Michel Marcus, Aug 30 2017 CROSSREFS Cf. A000040, A000043, A006530, A016047, A020639, A236128. Contains A002515. Sequence in context: A095080 A229289 A087634 * A178576 A038970 A079149 Adjacent sequences:  A291688 A291689 A291690 * A291692 A291693 A291694 KEYWORD nonn AUTHOR Thomas Ordowski, Aug 30 2017 EXTENSIONS a(17)-a(26) from Michel Marcus, Aug 30 2017 a(27)-a(34) from Giovanni Resta, Aug 30 2017 a(35)-a(52) from Charles R Greathouse IV, Aug 30 2017 STATUS approved

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Last modified May 13 06:11 EDT 2021. Contains 343836 sequences. (Running on oeis4.)