A242102 Semiprimes that are the concatenation of a prime and the previous prime.
1713, 2319, 2923, 4341, 6159, 7167, 8983, 103101, 151149, 157151, 163157, 167163, 173167, 191181, 197193, 233229, 257251, 277271, 283281, 311307, 337331, 367359, 373367, 421419, 431421, 439433, 449443, 463461, 467463, 479467, 487479, 509503, 521509, 547541, 557547
Offset: 1
Examples
13 and 17 are consecutive primes. Their reverse concatenation = 1713 = 3 * 571, which is semiprime. 19 and 23 are consecutive primes. Their reverse concatenation = 2319 = 3 * 773, which is semiprime.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..11480
Programs
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Maple
select(k -> numtheory:-bigomega(k)=2, [seq(parse(cat(ithprime(n+1),ithprime(n))), n=1..200)]);
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Mathematica
A242102 = {}; Do[t = FromDigits[Flatten[IntegerDigits /@ {Prime[n], Prime[n - 1]}]]; If[PrimeOmega[t] == 2, AppendTo[A242102, t]], {n, 2, 200}]; A242102
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PARI
forprime(p=1,10^3,q=concat(Str(p),Str(precprime(p-1)));if(bigomega(eval(q))==2,print1(eval(q),", "))) \\ Derek Orr, Aug 15 2014