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A276803
Semiprimes k such that the concatenation of its prime factors is prime.
1
6, 21, 22, 33, 39, 46, 51, 58, 82, 93, 111, 115, 133, 141, 142, 159, 166, 177, 187, 201, 205, 219, 226, 235, 237, 247, 249, 253, 262, 267, 274, 291, 301, 319, 327, 355, 358, 391, 411, 427, 478, 489, 501, 502, 505, 511, 535, 538, 543, 562, 565, 573, 583, 586, 589
OFFSET
1,1
COMMENTS
Alternatively: Semiprimes p*q, with p<q, such that the concatenation p || q is a prime.
Corresponding primes are at A105184.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
21 is a term because 21 = 3 * 7 that is a semiprime : concatenation of 3 and 7 = 37 which is prime.
142 is a term because 142 = 2 * 71 that is a semiprime : concatenation of 2 and 71 = 271 which is prime.
MATHEMATICA
Select[Select[Range[1000], PrimeOmega[#] == 2 &], PrimeQ[FromDigits[Join[IntegerDigits [First@First[FactorInteger[#]]], IntegerDigits[First@Last[FactorInteger[#]]]]]] &]
Select[Range[1000], PrimeOmega[#]==PrimeNu[#]==2&&PrimeQ[FromDigits[ Flatten[ IntegerDigits/@FactorInteger[#][[All, 1]]]]]&] (* Harvey P. Dale, Aug 03 2022 *)
PROG
(PARI) list(lim)=my(v=List()); forprime(p=2, lim\2, forprime(q=2, min(p, lim\p), if(isprime(eval(Str(q, p))), listput(v, p*q)))); Set(v) \\ Charles R Greathouse IV, Sep 17 2016
CROSSREFS
KEYWORD
nonn,base
AUTHOR
K. D. Bajpai, Sep 17 2016
STATUS
approved