A212769 p*q modulo (p+q) with p, q consecutive primes.

1, 7, 11, 5, 23, 11, 35, 17, 43, 59, 59, 35, 83, 41, 91, 103, 119, 119, 65, 143, 143, 77, 163, 77, 95, 203, 101, 215, 107, 191, 125, 259, 275, 263, 299, 299, 311, 161, 331, 343, 359, 347, 383, 191, 395, 169, 181, 221, 455, 227, 463, 479, 467, 499, 511, 523

Offset

1,2

Comments

Graph consists of two branches, the upper one corresponds to cases (q-p) = 2 (mod 4), and the lower one to cases (q-p) = 0 (mod 4).

If prime(n+k) = prime(n)+4*k^2 for k=1..m, then a(n)=...=a(n+m-1)=2*prime(n)+1. - Robert Israel, Jan 20 2022

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Formula

From Robert Israel, Jan 20 2022: (Start)

If prime(n+1)-prime(n) = 4*k+2 with k^2 <= prime(n)/2, then a(n) = 2*prime(n)-4*k^2+1.

If prime(n+1)-prime(n) = 4*k with 4*k^2+2*k<prime(n), then a(n) = prime(n) - 4*k^2 + 2*k. (End)

Maple

f:= proc(n) local p, q;
  p:= ithprime(n); q:= nextprime(p);
  (p*q) mod (p+q)
end proc:
map(f, [$1..100]); # Robert Israel, Jan 20 2022

Mathematica

Mod[Times@@#, Total[#]]&/@Partition[Prime[Range[60]], 2, 1] (* Harvey P. Dale, Feb 21 2022 *)

Prog

(PARI) a(n) = (prime(n)*prime(n+1)) % (prime(n)+prime(n+1)); \\ Michel Marcus, Oct 19 2013
(PARI) a(n)=my(p=prime(n), q=nextprime(p+1)); (p*q)%(p+q) \\ Charles R Greathouse IV, Oct 19 2013

Crossrefs

Sequence in context: A144076 A113492 A097152 * A269485 A228954 A283651

Adjacent sequences: A212766 A212767 A212768 * A212770 A212771 A212772

Keyword

nonn

Author

Zak Seidov, May 26 2012

Status

approved