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A119748
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Numbers that are not the sum of a prime and a (nontrivial, positive) power.
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3
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OFFSET
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1,2
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COMMENTS
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From a question raised by Tanya Khovanova.
1771561 = 11^6 is the first composite number here. - T. D. Noe, Sep 29 2011
James Van Buskirk and John Robertson report that these are the only terms known up to 10^10. - Charles R Greathouse IV, Jan 30 2014
Hardy & Littlewood's Conjecture H implies that there are finitely many nonsquare terms in this sequence. Wang's result implies that a(n) >> n^1.018. - Charles R Greathouse IV, May 28 2015
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REFERENCES
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G. H. Hardy, J. E. Littlewood, Some of the problems of partitio numerorum III: On the expression of a large number as a sum of primes, Acta Mathematica 44 (1923), pp. 1-70.
Wang Tianze, On the exceptional set for the equation n = p + k^2, Acta Mathematica Sinica 11 (1995), pp. 156-167.
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LINKS
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Table of n, a(n) for n=1..5.
John Robertson, Integers of the form x^2+kp (1999)
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PROG
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(PARI) is(n)=for(e=2, log(n)\log(2), for(b=2, sqrtnint(n, e), if(isprime(n-b^e)&&!ispower(b), return(0)))); 1 \\ Charles R Greathouse IV, May 28 2015
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CROSSREFS
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Cf. A119747.
Sequence in context: A078748 A051131 A306785 * A101341 A079014 A215436
Adjacent sequences: A119745 A119746 A119747 * A119749 A119750 A119751
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KEYWORD
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nonn,more
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AUTHOR
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David W. Wilson, Jul 30 2006
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EXTENSIONS
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1771561 from Max Alekseyev, Jul 31 2006
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STATUS
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approved
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