A258214 Primes formed by concatenating p^2 with q, where p, q are consecutive primes.

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

K. D. Bajpai, Table of n, a(n) for n = 1..10000

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

Cf. A000040, A030461, A030469.

Sequence in context: A142450 A259421 A202008 * A262915 A262330 A142632

Adjacent sequences: A258211 A258212 A258213 * A258215 A258216 A258217

Keyword

nonn,base

Author

K. D. Bajpai, May 23 2015

Status

approved