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A258214
Primes formed by concatenating p^2 with q, where p, q are consecutive primes.
1
43, 257, 12113, 84131, 96137, 168143, 372167, 32041181, 120409349, 139129379, 292681547, 410881643, 516961727, 528529733, 863041937, 966289991, 10629611033, 10670891039, 11902811093, 16307291279, 21112091459, 25058891597, 29618411723, 31933691789, 35006411873
OFFSET
1,1
COMMENTS
All the terms in this sequence, except a(1), are congruent to 2 (mod 3).
LINKS
EXAMPLE
a(2) = 257 is prime formed by concatenation of (5^2) = 25 with 7.
a(3) = 12113 is prime formed by concatenation of (11^2) = 121 with 13.
MATHEMATICA
Select[Table[p = Prime[n]; FromDigits[Join[Flatten[ IntegerDigits[{p^2, NextPrime[p]}]]]], {n, 500}], PrimeQ]
Select[#[[1]]^2*10^IntegerLength[#[[2]]]+#[[2]]&/@Partition[Prime[ Range[ 300]], 2, 1], PrimeQ] (* Harvey P. Dale, Dec 05 2016 *)
PROG
(PARI) forprime(p = 1, 5000, k=eval(concat( Str(p^2), Str(nextprime(p+1)) )); if(isprime(k), print1(k, ", ")))
(Magma) [m: n in [1..300] | IsPrime(m) where m is Seqint(Intseq(NthPrime(n+1)) cat Intseq(NthPrime(n)^2))]; // Vincenzo Librandi, May 24 2015
CROSSREFS
KEYWORD
nonn,base
AUTHOR
K. D. Bajpai, May 23 2015
STATUS
approved