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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. 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 (list; graph; refs; listen; history; text; internal format)
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: A246930 A142525 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

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Last modified August 8 08:38 EDT 2022. Contains 356003 sequences. (Running on oeis4.)