A072565 a(n) = prime(n+1)*prime(n+2)+1 mod prime(n), where prime(n) is the n-th prime.

0, 0, 3, 4, 2, 12, 13, 3, 3, 17, 30, 25, 13, 41, 26, 49, 17, 0, 25, 17, 61, 41, 2, 8, 25, 13, 25, 13, 73, 27, 41, 49, 25, 121, 17, 73, 61, 41, 73, 49, 25, 121, 13, 25, 29, 90, 193, 25, 13, 41, 49, 25, 161, 73, 73, 49, 17, 61, 25, 25, 241, 253, 25, 13, 73, 281, 97, 121, 13

Offset: 1

Author

G. L. Honaker, Jr., Aug 06 2002

Keywords

• nonn

Examples

			a(18) = prime(19)*prime(20)+1 mod prime(18) = 67*71+1 mod 61 = 0.
		

References

• R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer-Verlag, NY, (2002 printing), Research problem 1.85, p. 73.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000040, A023523, A022461.

Programs

GAP

P:=Filtered([1..1000],IsPrime);;
List([1..70],n->(P[n+1]*P[n+2]+1) mod P[n]); # Muniru A Asiru, Mar 09 2018

Magma

[(NthPrime(n+1)*NthPrime(n+2)+1) mod NthPrime(n): n in [1..100]]; // Vincenzo Librandi, Feb 28 2018

Maple

p:=ithprime; seq((p(n+1)*p(n+2)+1) mod p(n),n=1..70); # Muniru A Asiru, Mar 09 2018

Mathematica

a[n_] := Mod[Prime[n+1] Prime[n+2] + 1, Prime[n]]
Mod[#[[2]]#[[3]]+1,#[[1]]]&/@Partition[Prime[Range[80]],3,1] (* Harvey P. Dale, Dec 19 2018 *)

PARI

a(n) = (prime(n+1)*prime(n+2) + 1) % prime(n); \\ Michel Marcus, Feb 28 2018

Formula

a(n) = A023523(n+1) mod A000040(n). - Michel Marcus, Feb 28 2018

Extensions

Edited by Dean Hickerson and Robert G. Wilson v, Aug 10 2002