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 A236747 Number of 0 <= k <= sqrt(n) such that n-k and n+k are both prime. 3
 0, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 1, 2, 1, 1, 1, 0, 2, 1, 0, 1, 0, 0, 2, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 2, 2, 0, 1, 1, 1, 1, 2, 0, 2, 1, 1, 1, 1, 0, 2, 0, 1, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Probably a(n) > N for any N and all sufficiently large n. Perhaps a(2591107) is the last 0 in this sequence. - Charles R Greathouse IV, Jan 30 2014 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{k=0..A000196(n)} (A010051(n-k) * A010051(n+k)). - Antti Karttunen, Feb 01 2014 EXAMPLE a(3) = 1 because 3 - 0 = 3 and 3 + 0 = 3 are both prime for k = 0; a(4) = 1 because 4 - 1 = 3 and 4 + 1 = 5 are both prime for k = 1 < sqrt(4) = 2; a(5) = 2 because 5 - 0 = 5 and 5 + 0 = 5 are both prime for k = 0, 5 - 2 = 3 and 5 + 2 = 7 are both prime for k = 2 < sqrt(5). MATHEMATICA Table[Length[Select[Range[0, Sqrt[n]], PrimeQ[n - #] && PrimeQ[n + #] &]], {n, 100}] (* T. D. Noe, Feb 01 2014 *) PROG (PARI) a(n)=sum(k=0, sqrtint(n), isprime(n-k)&&isprime(n+k)) \\ Charles R Greathouse IV, Jan 30 2014 (Scheme) (define (A236747 n) (add (lambda (k) (* (A010051 (- n k)) (A010051 (+ n k)))) 0 (A000196 n))) ;; The following implements sum_{i=lowlim..uplim} intfun(i): (define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i))))))) ;; From Antti Karttunen, Feb 01 2014 CROSSREFS Cf. A000196, A010051, A061357, A171637. Sequence in context: A073490 A279907 A225654 * A194285 A135341 A033665 Adjacent sequences:  A236744 A236745 A236746 * A236748 A236749 A236750 KEYWORD nonn AUTHOR Juri-Stepan Gerasimov, Jan 30 2014 EXTENSIONS Terms recomputed (with corrections) by Antti Karttunen, Feb 01 2014 STATUS approved

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Last modified November 13 00:25 EST 2019. Contains 329083 sequences. (Running on oeis4.)