A191913 Products of two distinct primes such that a concatenation of the factors (p||q or q||p) again is a product of two distinct primes.

15, 26, 34, 35, 38, 39, 55, 57, 69, 74, 85, 87, 91, 94, 95, 106, 115, 118, 119, 123, 134, 141, 145, 159, 161, 185, 187, 202, 205, 206, 209, 213, 215, 217, 221, 237, 254, 259, 265, 267, 287, 291, 295, 298, 301, 303, 309, 314, 319, 321, 334, 339, 346, 362, 365, 371, 377, 381, 382, 391, 393, 395, 398, 403, 407, 413, 415, 417, 437, 445

Offset

1,1

Comments

A subsequence of A191912. Contains A191915 as a subsequence.

Inspired by the calculation of sphenic chains, cf. link.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

D. Broadhurst (in reply to James Merickel), Re: Sphenic chain by concatenation of factors, "primenumbers" group, June 16, 2011.

James Merickel, David Broadhurst, Kevin Acres, Sphenic tree by factor concatenation on 114, digest of 16 messages in primenumbers Yahoo group, Jun 11, 2011 - Jun 23, 2011.

Example

26=2*13 is in the sequence because 213 =3*71 is a product of two distinct primes.

Mathematica

tdpQ[n_]:=Module[{fi=FactorInteger[n][[All, 1]]}, AnyTrue[ {fi[[1]]* 10^IntegerLength[fi[[2]]]+ fi[[2]], fi[[2]]*10^IntegerLength[ fi[[1]]]+ fi[[1]]}, PrimeNu[#]==PrimeOmega[#]==2&]]; Select[Range[ 500], PrimeOmega[#] == PrimeNu[#]==2&&tdpQ[#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 20 2018 *)

Prog

(PARI) for(i=1, 500, is_A006881(i)|next; f=factor(i); is_A006881(eval(Str(f[1, 1], f[2, 1]))) | is_A006881(eval(Str(f[2, 1], f[1, 1]))) & print1(i", "))

Crossrefs

Cf. A006881.

Sequence in context: A249109 A342221 A074974 * A191915 A359547 A189045

Adjacent sequences: A191910 A191911 A191912 * A191914 A191915 A191916

Keyword

nonn,base

Author

M. F. Hasler, Jun 19 2011

Status

approved