A130096 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 not primes.

31, 47, 59, 71, 79, 83, 101, 107, 113, 127, 131, 149, 151, 157, 173, 193, 211, 223, 229, 233, 271, 311, 317, 337, 347, 349, 373, 383, 389, 401, 439, 457, 461, 467, 487, 491, 509, 521, 523, 541, 563, 569, 571, 593, 647, 653, 661, 683, 709, 727, 733, 743, 773

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..2500

Example

a(1)=31 because (37^2 - 31^2)/2 - 1 = 203 and (37^2 - 31^2)/2 + 1 = 205 (203, 205 are not primes),
a(2)=47 because (53^2 - 47^2)/2 - 1 = 299 and (53^2 - 47^2)/2 + 1 = 301 (299, 301 are not primes),
a(3)=59 because (61^2 - 59^2)/2 - 1 = 119 and (61^2 - 59^2)/2 + 1 = 121 (119, 121 are not primes), ...

Maple

ts_p3_21:=proc(n) local a, b, i, ans; ans := [ ]: for i from 2 to n do a := (ithprime(i+1)^(2)-ithprime(i)^(2))/2-1: b := (ithprime(i+1)^(2)-ithprime(i)^(2))/2+1: if not (isprime(a)=true or isprime(b)=true) then ans := [ op(ans), ithprime(i) ]: fi od; RETURN(ans) end: ts_p3_21(500);

Mathematica

Transpose[Select[Partition[Prime[Range[2, 250]], 2, 1], PrimeQ[(#[[2]]^2- #[[1]]^2)/2+{1, -1}]=={False, False}&]][[1]] (* Harvey P. Dale, Jun 19 2014 *)
Select[Partition[Prime[Range[2, 150]], 2, 1], NoneTrue[(#[[2]]^2- #[[1]]^2)/ 2+{1, -1}, PrimeQ]&][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 10 2021 *)

Crossrefs

Cf. A130761.

Sequence in context: A046047 A014313 A095318 * A229624 A270781 A075586

Adjacent sequences: A130093 A130094 A130095 * A130097 A130098 A130099

Keyword

nonn

Author

Jani Melik, Aug 01 2007

Status

approved