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

0,1

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." [Warning: As of March 2018 this site appears to have been hacked. Proceed with great caution. The original content should be retrieved from the Wayback machine and added here. - N. J. A. Sloane, Mar 29 2018]

Formula

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

Mathematica

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

Crossrefs

Cf. A023201, A046117.

Cf. A000040, A103195.

Sequence in context: A345363 A242218 A051985 * A277172 A023691 A045118

Adjacent sequences: A103203 A103204 A103205 * A103207 A103208 A103209

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Mar 19 2005

Status

approved