A130056 Primes prime(n) such that both of the numbers (prime(n+2)^2-prime(n)^2)/2 - 1 and (prime(n+2)^2-prime(n)^2)/2 + 1 are primes.

7, 19, 37, 61, 67, 71, 97, 107, 127, 157, 229, 349, 419, 443, 673, 743, 751, 877, 937, 947, 967, 1009, 1039, 1063, 1553, 1609, 1637, 1913, 2311, 2381, 2417, 2437, 2687, 2753, 2969, 3067, 3079, 3137, 3313, 3559, 3803, 3911, 3919, 4111, 4157, 4507, 4621

Offset

1,1

Links

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

Example

a(1)=7 because (13^2 - 7^2)/2 - 1 = 59 and (13^2 - 7^2)/2 + 1 = 61 (59, 61 are both primes),
a(2)=19 because (29^2 - 19^2)/2 - 1 = 239 and (29^2 - 19^2)/2 + 1 = 241,
a(3)=37 because (43^2 - 37^2)/2 - 1 = 239 and (43^2 - 37^2)/2 + 1 = 241, ...

Maple

ts_p4:=proc(n) local a, b, i, ans; ans := [ ]: for i from 2 by 1 to n do a := (ithprime(i+2)^(2)-ithprime(i)^(2))/2-1: b := (ithprime(i+2)^(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_p4(2000);

Mathematica

Prime/@Select[Range[700], AllTrue[(Prime[#+2]^2-Prime[#]^2)/2+{1, -1}, PrimeQ]&] (* Harvey P. Dale, Nov 27 2022 *)

Crossrefs

Cf. A130761.

Sequence in context: A152540 A073859 A038847 * A136057 A177092 A023224

Adjacent sequences: A130053 A130054 A130055 * A130057 A130058 A130059

Keyword

nonn

Author

Jani Melik, Aug 01 2007

Status

approved