A268033 Numbers n such that concatenating prime(n) with n^2 is prime.

3, 9, 11, 29, 33, 39, 121, 153, 177, 179, 187, 193, 207, 231, 261, 291, 357, 361, 423, 471, 487, 507, 543, 579, 621, 627, 633, 641, 659, 683, 699, 737, 773, 843, 863, 879, 907, 933, 957, 1009, 1011, 1023, 1049, 1051, 1099, 1101, 1107, 1131, 1191, 1327, 1387, 1403

Offset

1,1

Comments

All the terms in this sequence are odd numbers.

Links

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

Example

9 appears in the sequence because prime(9) || 9^2 = 2381 which is prime.
11 appears in the sequence because prime(11) || 11^2 = 31121 which is prime.

Maple

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

Mathematica

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

Prog

(PARI) for (n = 1, 1000, if(isprime(k=eval(Str(prime(n), n^2))), print1(n, ", ")))
(Magma) [n:n in[1..500]|IsPrime(m) where m is Seqint(Intseq(n^2) cat Intseq(NthPrime(n)))];

Crossrefs

Cf. A000040, A000290.

Sequence in context: A272704 A272737 A273533 * A145812 A220944 A200879

Adjacent sequences: A268030 A268031 A268032 * A268034 A268035 A268036

Keyword

nonn,base

Author

K. D. Bajpai, Jan 24 2016

Status

approved