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A103206 Concatenations of pairs of primes that differ by 6. 8
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 (list; graph; refs; listen; history; text; internal format)
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."

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: A145588 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

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Last modified March 27 16:36 EDT 2017. Contains 284177 sequences.