login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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