A130066 Primes prime(n) such that both of the numbers (prime(n+1)^2-prime(n)^2)/2 - 1 and (prime(n+1)^2-prime(n)^2)/2 + 1 are primes.

5, 13, 29, 43, 103, 163, 167, 421, 547, 557, 587, 631, 659, 691, 701, 809, 823, 883, 919, 977, 1249, 1367, 1459, 1499, 1637, 1663, 1693, 1747, 1801, 1889, 1987, 2129, 2203, 2549, 2719, 3089, 3137, 3221, 3329, 3389, 3637, 3881, 4327, 4507, 4513, 4663, 4783

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

a(1)=5 because (7^2 - 5^2)/2 - 1 = 11 and (7^2 - 5^2)/2 + 1 = 13 (11, 13 are both primes),
a(2)=13 because (17^2 - 13^2)/2 - 1 = 59 and (17^2 - 13^2)/2 + 1 = 61,
a(3)=29 because (31^2 - 29^2)/2 - 1 = 59 and (31^2 - 29^2)/2 + 1 = 61, ...

Maple

ts_p3_1:=proc(n) local a, b, i, ans; ans := [ ]: for i from 2 by 1 to n do a := (ithprime(i+1)^(2)-ithprime(i)^(2))/2-1: b := (ithprime(i+1)^(2)-ithprime(i)^(2))/2+1: if (isprime(a)=true and isprime(b)=true) then ans := [ op(ans), ithprime(i) ]: fi od; RETURN(ans) end: ts_p3_1(2000);

Mathematica

Transpose[Select[Partition[Prime[Range[1000]], 2, 1], AllTrue[(#[[2]]^2- #[[1]]^2)/2+ {1, -1}, PrimeQ]&]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 03 2015 *)

Crossrefs

Cf. A130761.

Sequence in context: A247177 A146286 A065374 * A206258 A270106 A304904

Adjacent sequences: A130063 A130064 A130065 * A130067 A130068 A130069

Keyword

nonn

Author

Jani Melik, Aug 01 2007

Status

approved