

A038458


Decimal expansion of the solution to 127^x  113^x = 1, sometimes called the Smarandache constant. 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
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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


REFERENCES

Octavian Cira, Smarandache's Conjecture on Consecutive Primes, International J. Math. Combin. Vol. 4 (2014), 6991; http://mathcombin.com/upload/file/20150127/1422320940239094100.pdf#page=74


LINKS

Harry J. Smith, Table of n, a(n) for n = 0..20000
M. L. Perez, Five Smarandache Conjectures On Primes, Arizona State University, Special Collections.
F. Smarandache, Conjectures which Generalize Andrica's Conjecture, Octogon, Vol. 7, No. 1, 173176, 1999.
Eric Weisstein's World of Mathematics, Andrica's Conjecture
Eric Weisstein's World of Mathematics, Smarandache Constants


EXAMPLE

0.567148130202017714646846875533482564586790249388638206840285221826806766338276...


PROG

(PARI) { default(realprecision, 20080); x=solve(x=.5, .6, 127^x113^x1); d=0; for (n=0, 20000, x=(xd)*10; d=floor(x); write("b038458.txt", n, " ", d)); } \\ Harry J. Smith, Apr 13 2009


CROSSREFS

Sequence in context: A214681 A019978 A030178 * A267017 A021642 A171423
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



