A384638 Primes p such that the concatenations of three consecutive primes starting with p, in both forward and backwards orders, are triprimes.
43, 47, 97, 101, 151, 157, 167, 199, 281, 293, 487, 601, 607, 809, 839, 967, 1013, 1069, 1129, 1223, 1249, 1259, 1289, 1361, 1367, 1543, 1571, 1663, 1753, 1861, 1871, 1873, 1997, 2141, 2281, 2551, 2593, 2909, 3121, 3271, 3313, 3361, 3371, 3461, 3823, 3881, 3907, 4019, 4211, 4289, 4327, 4349, 4451, 4513
Offset: 1
Examples
a(2) = 47 is a term because 47, 53, 59 are consecutive primes and both 475359 = 3 * 193 * 821 and 595347 = 3 * 191 * 1039 have three prime factors, counted with multiplicity.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
cat3:= proc(a,b,c) (a*10^(1+ilog10(b))+b)*10^(1+ilog10(c))+c end proc; R:= NULL: count:= 0: a:= 2: b:= 3: c:= 5: for i from 1 while count < 100 do a:= b; b:= c; c:= nextprime(c); if numtheory:-bigomega(cat3(a,b,c)) = 3 and numtheory:-bigomega(cat3(c,b,a)) = 3 then R:= R,a; count:= count+1; fi od: R; -
Mathematica
Select[Prime[Range[612]],PrimeOmega[FromDigits[Join[IntegerDigits[#],IntegerDigits[NextPrime[#]],IntegerDigits[NextPrime[#,2]]]]]==3&&PrimeOmega[FromDigits[Join[IntegerDigits[NextPrime[#,2]],IntegerDigits[NextPrime[#,1]],IntegerDigits[#]]]]==3&] (* James C. McMahon, Jun 20 2025 *)
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