A090120 Numbers k such that nextprime(k^2) - prevprime(k^2) = 4.

3, 4, 9, 10, 14, 15, 20, 21, 26, 33, 40, 110, 117, 124, 146, 206, 237, 250, 273, 303, 309, 326, 340, 350, 387, 429, 436, 440, 441, 447, 470, 513, 561, 573, 609, 634, 686, 704, 807, 897, 920, 1004, 1035, 1054, 1060, 1071, 1113, 1124, 1143, 1156, 1233, 1239

Offset: 1

Author

Labos Elemer, Jan 09 2004

Keywords

• nonn

Comments

Note that the gap = 4 is partitioned either as 2+2 or as 3+1; 1+3 never occurs since n^2-1 is composite if n>2.

Examples

			k = 3 is a term since, k^2 = 9 is surrounded by the closest primes: {7,[9],11}.
k = 10 is a term since k^2 = 100 is surrounded by {97,[100],101}.
		

Links

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

Crossrefs

Cf. A090116, A090117, A090118, A090119, A007917, A007918, A000720, A000040, A053001, A007491, A000290.

Programs

Mathematica

Select[Range[3,1500], NextPrime[#^2] == NextPrime[#^2, -1] + 4 &] (* Giovanni Resta, May 26 2018 *)

PARI

isok(n) = nextprime(n^2) - precprime(n^2) == 4; \\ Michel Marcus, May 26 2018

Formula

Solutions to {x; A007918(x^2)-A007917(x^2) = 4}.