A103206 Concatenations of pairs of primes that differ by 6.

511, 713, 1117, 1319, 1723, 2329, 3137, 3743, 4147, 4753, 5359, 6167, 6773, 7379, 8389, 97103, 101107, 103109, 107113, 131137, 151157, 157163, 167173, 173179, 191197, 193199, 223229

Offset: 0

Author

Jonathan Vos Post, Mar 19 2005

Keywords

• base
• easy
• nonn

Comments

Prime in this sequence: a(3) = 1117, a(4) = 1319, a(5) = 1723, a(7) = 3137, a(15) = 8389, a(16) = 97103, a(17) = 101107, a(21) = 151157, a(22) = 157163, a(23) = 167173, a(27) = 223229. Semiprimes in this sequence: a(1) = 511 = 7 x 73, a(2) = 713 = 23 * 31, a(6) = 2329 = 17 * 137, a(8) = 3743 = 19 * 197, a(11) = 5359 = 23 * 233, a(12) = 6167 = 7 * 881, a(13) = 6773 = 13 * 521, a(14) = 7379 = 47 x 157, a(18) = 103109 = 23 * 4483, a(20) = 131137 = 71 * 1847, a(26) = 193199 = 43 * 4493, ... Note that a(9) = 4147 = 11 * 13 * 29 and a(19) = 107113 = 43 * 47 * 53 are the products of three primes with the same number of digits.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Sexy Primes.
• T. Trotter, "Sexy Primes."

Crossrefs

Cf. A023201, A046117.

Cf. A000040, A103195.

Programs

Mathematica

FromDigits[Flatten[IntegerDigits/@{#,#+6}]]&/@Select[Prime[Range[50]], PrimeQ[#+6]&] (* Harvey P. Dale, Jun 24 2015 *)

Formula

a(n) = A023201(n) concatenated with A023201(n)+6.