A154963 Primes p such that the concatenation of p and prime(p) is prime.
2, 17, 23, 41, 61, 71, 83, 127, 227, 337, 353, 499, 503, 571, 727, 887, 911, 937, 971, 1061, 1427, 1579, 1663, 1693, 1709, 1871, 1877, 1907, 1949, 1973, 2017, 2063, 2081, 2239, 2339, 2393, 2467, 2713, 2797, 2939, 2999, 3181, 3271, 3463, 3643, 3659, 3677
Offset: 1
Examples
Concatenation of prime 2 and second prime 3 is the prime 23, hence 2 is in the sequence. Concatenation of prime 23 and 23rd prime 83 is the prime 2383, hence 23 is in the sequence.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Programs
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Magma
[ p: p in PrimesUpTo(3700) | IsPrime(StringToInteger(IntegerToString(p) cat IntegerToString(NthPrime(p)))) ];
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Mathematica
A154963 = Select[ Prime[ Range[ 550 ] ], PrimeQ[ FromDigits[ Join[ IntegerDigits[ # ], IntegerDigits[ Prime[ # ] ] ] ] ] & ] (* Alonso del Arte Nov 12 2009 *)
Extensions
Edited and extended beyond a(3) by Klaus Brockhaus, Jan 20 2009