A172462 Numbers k such that 2k-3, 2k-1, 2k+1 and 2k+3 are composite.

59, 60, 61, 72, 93, 102, 103, 108, 109, 123, 144, 149, 150, 151, 161, 162, 163, 171, 207, 213, 236, 237, 257, 258, 264, 265, 266, 267, 268, 276, 291, 312, 313, 318, 333, 334, 348, 357, 389, 390, 391, 396, 401, 402, 408, 417, 422, 423, 424, 434, 435, 436, 446

Offset: 1

Author

Juri-Stepan Gerasimov, Feb 03 2010

Keywords

• nonn
• easy
• less

Comments

Almost all numbers are in this sequence, by the Prime Number Theorem.

Examples

			a(1)=59 because 2*59-1=117, 2*59+1=119, 2*59-3=115 and 2*59+3=121 are all composite.
		

Crossrefs

Cf. A104278.

Programs

Maple

a := proc (n): if isprime(2*n-3) = false and isprime(2*n-1) = false and isprime(2*n+1) = false and isprime(2*n+3) = false then n else end if end proc: seq(a(n), n = 1 .. 500); # Emeric Deutsch, Feb 15 2010

Extensions

Corrected and extended by Emeric Deutsch, Feb 15 2010

Comment from Charles R Greathouse IV, Mar 25 2010