A119748 - OEIS

A119748

Numbers that are not the sum of a prime and a (nontrivial, positive) power.

1, 2, 5, 1549, 1771561 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`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`
	LINKS	`Table of n, a(n) for n=1..5.` `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.` `John Robertson, Integers of the form x^2+kp (1999). [Broken link]` `Wang Tianze, On the exceptional set for the equation n = p + k^2, Acta Mathematica Sinica, Vol. 11, No. 2 (1995), pp. 156-167.`
	PROG	`(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`
	CROSSREFS	`Cf. A119747.` `Sequence in context: A078748 A051131 A306785 * A101341 A079014 A215436` `Adjacent sequences: A119745 A119746 A119747 * A119749 A119750 A119751`
	KEYWORD	`nonn,more`
	AUTHOR	`David W. Wilson, Jul 30 2006`
	EXTENSIONS	`1771561 from Max Alekseyev, Jul 31 2006`
	STATUS	`approved`

Last modified August 29 11:15 EDT 2024. Contains 375512 sequences. (Running on oeis4.)