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A038458
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Consider the equation q^x-p^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.
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5
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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
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0,1
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COMMENTS
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Sometimes called the Smarandache constant.
Is this constant rational or irrational? I conjecture it is irrational. - Sukanto Bhattacharya (susant5au(AT)yahoo.com.au), Apr 28 2008
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REFERENCES
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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, 173-176, 1999.
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 0..20000
Eric Weisstein's World of Mathematics, Andrica's Conjecture
Eric Weisstein's World of Mathematics, Smarandache Constant
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EXAMPLE
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Generalizes Andrica's conjecture p(n+1)^(1/2)-p(n)^(1/2)<1 to p(n+1)^a-p(n)^a<1 if a < this number.
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PROG
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(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)); } [From Harry J. Smith, Apr 13 2009]
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CROSSREFS
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Sequence in context: A214681 A019978 A030178 * A021642 A101288 A212479
Adjacent sequences: A038455 A038456 A038457 * A038459 A038460 A038461
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KEYWORD
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nonn,cons
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AUTHOR
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M. I. Petrescu (mipetrescu(AT)yahoo.com)
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STATUS
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approved
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