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A236747
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Number of 0 <= k <= sqrt(n) such that n-k and n+k are both prime.
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3
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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
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OFFSET
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1,5
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COMMENTS
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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
Primes p such that a(p)=1: 2, 3, 7, 11, 13, 17, 19, ... . Juri-Stepan Gerasimov, Feb 02 2014
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = Sum_{k=0..A000196(n)} (A010051(n-k) * A010051(n+k)). - Antti Karttunen, Feb 01 2014
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EXAMPLE
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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).
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MAPLE
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A236767 := proc(n)
local a, k ;
a := 0 ;
for k from 0 to floor(sqrt(n)) do
if isprime(n-k) and isprime(n+k) then
a := a+1 ;
end if;
end do:
a ;
end proc:
seq(A236767(n), n=1..80) ; # R. J. Mathar, Dec 01 2020
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MATHEMATICA
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Table[Length[Select[Range[0, Sqrt[n]], PrimeQ[n - #] && PrimeQ[n + #] &]], {n, 100}] (* T. D. Noe, Feb 01 2014 *)
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PROG
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(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
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CROSSREFS
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Cf. A000196, A010051, A061357, A171637.
Sequence in context: A073490 A279907 A225654 * A194285 A336676 A135341
Adjacent sequences: A236744 A236745 A236746 * A236748 A236749 A236750
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov, Jan 30 2014
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EXTENSIONS
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Terms recomputed (with corrections) by Antti Karttunen, Feb 01 2014
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STATUS
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approved
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