A117854 Let p(n) be the n-th-prime. Sequence gives primes of the form | p(n)*p(n+2) - p(n+1)*p(n+3)| +1.

37, 97, 61, 163, 199, 337, 353, 461, 379, 719, 1021, 421, 1753, 811, 577, 1607, 1423, 1949, 3121, 2141, 3943, 4549, 4243, 4969, 2801, 4261, 4357, 3767, 4621, 5647, 6917, 4603, 3697, 6491, 5653, 7019, 6841, 5153, 5261, 12163, 6121, 3301, 11587, 11887

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Formula

a(n) = | p(n)*p(n+2) - p(n+1)*p(n+3) | +1

Example

7, 11, 13, 17 --> | 7*13-11*17 | + 1 = 97
19, 23, 29, 31 --> | 19*29 - 23*31 | + 1 = 163

Maple

P:=proc(n) local i, j; for i from 1 by 1 to n do j:=abs(ithprime(i)*ithprime(i+2)-ithprime(i+1)*ithprime(i+3))+1; if isprime(j) then print(j); fi; od; end: P(1000);

Mathematica

Select[Abs[#[[1]]#[[3]]-#[[2]]#[[4]]]+1&/@Partition[ Prime[ Range[ 200]], 4, 1], PrimeQ] (* Harvey P. Dale, Oct 01 2015 *)

Crossrefs

Sequence in context: A142525 A368850 A132360 * A145480 A033222 A098025

Adjacent sequences: A117851 A117852 A117853 * A117855 A117856 A117857

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, May 02 2006

Status

approved