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 A038458 Decimal expansion of the solution to 127^x - 113^x = 1. This is the smallest x such that q^x - p^x = 1 for two successive primes p, q. 5
 5, 6, 7, 1, 4, 8, 1, 3, 0, 2, 0, 2, 0, 1, 7, 7, 1, 4, 6, 4, 6, 8, 4, 6, 8, 7, 5, 5, 3, 3, 4, 8, 2, 5, 6, 4, 5, 8, 6, 7, 9, 0, 2, 4, 9, 3, 8, 8, 6, 3, 8, 2, 0, 6, 8, 4, 0, 2, 8, 5, 2, 2, 1, 8, 2, 6, 8, 0, 6, 7, 6, 6, 3, 3, 8, 2, 7, 6, 9, 2, 1, 5, 0, 8, 8, 6, 9, 7, 3, 8, 5, 3, 6, 4, 2, 6, 4, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Generalizes Andrica's conjecture p(n+1)^(1/2) - p(n)^(1/2) < 1 to p(n+1)^c - p(n)^c < 1 if c is less than this number. Is this constant rational or irrational? I conjecture it is irrational. - Sukanto Bhattacharya (susant5au(AT)yahoo.com.au), Apr 28 2008 The first five digits are the same as the first five of A030178 = LambertW(1). - John W. Nicholson, Dec 11 2013 LINKS Harry J. Smith, Table of n, a(n) for n = 0..20000 Octavian Cira, Smarandache's conjecture on consecutive primes, International J. Math. Combin. 4 (2014), pp. 69-91. M. L. Perez, Five Smarandache conjectures on primes, Arizona State University, Special Collections. F. Smarandache, Conjectures which generalize Andrica's conjecture, Octogon 7:1 (1999), pp. 173-176. Eric Weisstein's World of Mathematics, Andrica's Conjecture Eric Weisstein's World of Mathematics, Smarandache Constants EXAMPLE 0.567148130202017714646846875533482564586790249388638206840285221826806766338276... MATHEMATICA RealDigits[x/.FindRoot[127^x-113^x==1, {x, 0.5}, WorkingPrecision->150]][[1]] (* Harvey P. Dale, Oct 24 2017 *) PROG (PARI) default(realprecision, 20080); x=solve(x=.5, .6, 127^x-113^x-1); d=0; for (n=0, 20000, x=(x-d)*10; d=floor(x); write("b038458.txt", n, " ", d)); \\ Harry J. Smith, Apr 13 2009 CROSSREFS Sequence in context: A214681 A019978 A030178 * A284361 A267017 A021642 Adjacent sequences:  A038455 A038456 A038457 * A038459 A038460 A038461 KEYWORD nonn,cons AUTHOR M. I. Petrescu (mipetrescu(AT)yahoo.com) EXTENSIONS Title improved, incorrect formula deleted, and other edits by M. F. Hasler, Jan 02 2015 STATUS approved

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