A271422 Concatenation of prime(n) and its square.

24, 39, 525, 749, 11121, 13169, 17289, 19361, 23529, 29841, 31961, 371369, 411681, 431849, 472209, 532809, 593481, 613721, 674489, 715041, 735329, 796241, 836889, 897921, 979409, 10110201, 10310609, 10711449, 10911881, 11312769, 12716129, 13117161, 13718769

Offset: 1

Author

Giovanni Teofilatto, Jul 13 2016

Keywords

• nonn
• easy
• base

Comments

All concatenations are divisible by the n-th prime.

a(n)/prime(n) gives a number of the form concatenate[(10^k)_prime(n)] for some k.

Subsequence of A053061.

Except for 24 and 525, a(n) have final decimal digit 1 or 9.

Examples

			For n=4, prime(4) = 7 (the fourth prime number) and 7^2 = 49. These are concatenated to get a(4) = 749. - _Michael B. Porter_, Jul 16 2016
		

Crossrefs

Cf. A001248 (primes squared), A030078 (primes cubed), A053061, A038800 (number of primes between 10n and 10n+9).

Programs

Maple

seq(n*(n+10^(1+ilog10(n^2))), n=select(k->isprime(k),[$1..137])); # Peter Luschny, Jul 16 2016

Mathematica

Table[FromDigits@ Flatten@ Map[IntegerDigits, {#, #^2}] &@ Prime@ n, {n, 33}] (* Michael De Vlieger, Jul 13 2016 *)

PARI

a(n) = eval(Str(prime(n), prime(n)^2)) \\ Felix Fröhlich, Jul 14 2016

Formula

a(n) = Concatenate [prime(n)_A001248(n)].

a(n) = p*(p+10^A055642(p^2)) with p = prime(n). - Peter Luschny, Jul 17 2016