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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 17 13:24 EDT 2022. Contains 353746 sequences. (Running on oeis4.)