A085451 -id:A085451 - cp's OEIS frontend

A045532 Concatenate n with n-th prime.

12, 23, 35, 47, 511, 613, 717, 819, 923, 1029, 1131, 1237, 1341, 1443, 1547, 1653, 1759, 1861, 1967, 2071, 2173, 2279, 2383, 2489, 2597, 26101, 27103, 28107, 29109, 30113, 31127, 32131, 33137, 34139, 35149, 36151, 37157, 38163, 39167, 40173, 41179, 42181

Offset: 1

Jeff Burch

Triangular numbers are 1653, 32131, 79401, ... - Ali Adams, Feb 04 2020

The next such terms are 173340627863131 and 1454987833022905581. - Giovanni Resta, Feb 04 2020

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000040, A075110.

Cf. A085451. [Reinhard Zumkeller, Jun 30 2010]

a045532 n = read $ show n ++ show (a000040 n) :: Integer
-- Reinhard Zumkeller, Jul 08 2014

[Seqint(Intseq(NthPrime(n)) cat Intseq(n)): n in [1..45]]; // Vincenzo Librandi, Apr 13 2019

Table[FromDigits[Join[IntegerDigits[n], IntegerDigits[Prime[n]]]], {n, 40}] (* Vincenzo Librandi, Apr 13 2019 *)
#[[1]]*10^IntegerLength[#[[2]]]+#[[2]]&/@Table[{n,Prime[n]},{n,50}] (* Harvey P. Dale, Oct 11 2024 *)

a(n) = eval(Str(n,prime(n))); \\ Michel Marcus, Apr 13 2019, simplified by M. F. Hasler, Feb 05 2020

from sympy import prime
def a(n): return int(str(n) + str(prime(n)))
print([a(n) for n in range(1, 43)]) # Michael S. Branicky, Dec 23 2021

a(n) = n*10^(A004216(A000040(n))+1) + A000040(n). - Reinhard Zumkeller, Sep 03 2002

A085453 Numbers n such that n^2 and n^3 together use only distinct digits.

Original entry on oeis.org

2, 3, 8, 9, 24, 69

Offset: 1

Zak Seidov, Jul 01 2003

There are only six such numbers (in base 10). Numbers with distinct digits in A010784. Primes with distinct digits in A029743. The case n and n^2 (exactly 22 numbers) in A059930. The case n and prime[n] (exactly 101 numbers) in A085451.

			69 is (the last) term because 69^2=4761 and 69^3=328509 together use all 10 distinct digits.

Cf. A010784 A029743 A059930 A085451

bb = {}; Do[idpn = IntegerDigits[n^3]; idn = IntegerDigits[n^2]; If[Length[idn] + Length[idpn] == Length[Union[idn, idpn]], bb = {bb, n}], {n, 1, 10000}]; Flatten[bb]

cp's OEIS Frontend

A045532 Concatenate n with n-th prime.

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