id:A062831 - OEIS Search Results

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Number of ways n can be expressed as the sum of a nonzero square and 1 or a prime.

+0
1

0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 0, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 0, 2, 3, 2, 1, 2, 0, 3, 2, 0, 2, 1, 1, 4, 2, 1, 2, 2, 1, 2, 2, 1, 3, 2, 1, 2, 2, 2, 2, 3, 1, 3, 2, 0, 2, 2, 0, 4, 2, 0, 3, 3, 2, 4, 2, 1, 2, 3, 1, 1, 3, 1, 4, 2, 1, 3, 1, 2, 5, 3, 0, 3, 3, 2, 2, 2, 0, 4, 2, 1, 3, 2, 1, 4, 1, 1, 3, 3 (list; graph; listen)

	OFFSET	`1,6`
	FORMULA	`Note that a(k^2)=0 or 1 since each prime can be written only in one way as a difference of squares: (n+b)^2-n^2=p where p is a prime, only if b^2+2nb=b(b+2n) is prime, only if b=1. In that case p=2n+1; since every prime is an odd number we get an 1 in the distribution of a(k^2) for each odd number which is prime.`
	MATHEMATICA	`a[n_] := Length[Select[n-Range[1, Floor[Sqrt[n]]]^2, #==1\|\|PrimeQ[ # ]&]]`
	CROSSREFS	`Sequence in context: A029434 A002217 A059342 this_sequence A037828 A030419 A096284` `Adjacent sequences: A062828 A062829 A062830 this_sequence A062832 A062833 A062834`
	KEYWORD	`nonn`
	AUTHOR	`Santi Spadaro (spados(AT)katamail.com), Jul 20 2001`
	EXTENSIONS	`Corrected and extended by Dean Hickerson, Jul 26, 2001`

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.

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