A074328 Numbers m such that prime(m^2+1)-prime(m^2)=2, where prime(j) is the j-th prime.

7, 8, 9, 12, 15, 16, 22, 25, 27, 34, 53, 83, 85, 88, 95, 107, 108, 144, 149, 187, 196, 223, 234, 238, 249, 255, 268, 274, 315, 324, 350, 355, 358, 367, 386, 410, 411, 416, 424, 436, 440, 445, 450, 462, 469, 471, 481, 494, 501, 509, 511, 517, 522, 549, 554, 564

Offset

1,1

Comments

Square roots of squares in A029707. - Michel Marcus, Oct 20 2022

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

25 is a term because the 626th and 625th primes are twin primes: 4639 - 4637 = 2.

Mathematica

t=Table[0, {250}]; t1=Table[0, {250}]; s=0; k=0; Do[s=Prime[1+n^2]-Prime[n^2]; If[s==2, k=k+1; t[[k]]=n; t1[[k]]=Prime[n^2]; Print[{k, n, Prime[n^2]}]], {n, 1, 2500}] t t1

Prog

(PARI) isok(m) = my(p=prime(m^2)); nextprime(p+1) - p == 2; \\ Michel Marcus, Oct 20 2022
(PARI) list(lim) = {my(k = 1, prv = 2); forprime(p = 3, lim, if(p - prv == 2 && issquare(k), print1(sqrtint(k), ", ")); k++; prv = p); } \\ Amiram Eldar, Mar 20 2025

Crossrefs

Cf. A029707, A001359, A006512, A011757.

Sequence in context: A030569 A192050 A045158 * A174185 A309152 A170933

Adjacent sequences: A074325 A074326 A074327 * A074329 A074330 A074331

Keyword

nonn

Author

Labos Elemer, Aug 21 2002

Status

approved