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

1,1

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.

Links

Table of n, a(n) for n=1..33.

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A047982 A210456 A095158 * A362148 A062374 A272593

Adjacent sequences: A271419 A271420 A271421 * A271423 A271424 A271425

Keyword

nonn,easy,base,changed

Author

Giovanni Teofilatto, Jul 13 2016

Status

approved