

A038458


Consider the equation q^xp^x=1 where p,q are successive primes; solve for x; the smallest such x is 0.567148... which occurs when p=113, q=127. Sequence gives decimal expansion of this value of x. Sometimes called the Smarandache constant.


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)^cp(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.  John W. Nicholson, Dec 11 2013


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 Constant [broken link]
Eric Weisstein's World of Mathematics, Smarandache Constants


FORMULA

a(n) = solve(p(n+1)^xp(n)^x < 1,x) with primes p(n+1) and p(n)


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)); } [From Harry J. Smith, Apr 13 2009]


CROSSREFS

Sequence in context: A214681 A019978 A030178 * A021642 A171423 A101288
Adjacent sequences: A038455 A038456 A038457 * A038459 A038460 A038461


KEYWORD

nonn,cons


AUTHOR

M. I. Petrescu (mipetrescu(AT)yahoo.com)


STATUS

approved



