A268033 - OEIS

%I #9 Sep 08 2022 08:46:15

%S 3,9,11,29,33,39,121,153,177,179,187,193,207,231,261,291,357,361,423,

%T 471,487,507,543,579,621,627,633,641,659,683,699,737,773,843,863,879,

%U 907,933,957,1009,1011,1023,1049,1051,1099,1101,1107,1131,1191,1327,1387,1403

%N Numbers n such that concatenating prime(n) with n^2 is prime.

%C All the terms in this sequence are odd numbers.

%H K. D. Bajpai, <a href="/A268033/b268033.txt">Table of n, a(n) for n = 1..10000</a>

%e 9 appears in the sequence because prime(9) || 9^2 = 2381 which is prime.

%e 11 appears in the sequence because prime(11) || 11^2 = 31121 which is prime.

%p select(n -> andmap(isprime, parse(cat(ithprime(n), n^2))), [seq(n, n=1..5000)]);

%t Select[Range[5000], PrimeQ[FromDigits[Flatten[{IntegerDigits[Prime[#]], IntegerDigits[#^2]}]]] &]

%o (PARI) for (n = 1,1000,if(isprime(k=eval(Str(prime(n),n^2))), print1(n, ", ")))

%o (Magma) [n:n in[1..500]|IsPrime(m) where m is Seqint(Intseq(n^2) cat Intseq(NthPrime(n)))];

%Y Cf. A000040, A000290.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Jan 24 2016