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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.
2
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
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
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Jun 19 2011
STATUS
approved