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Concatenate n with n-th prime.
14

%I #32 Oct 11 2024 14:58:11

%S 12,23,35,47,511,613,717,819,923,1029,1131,1237,1341,1443,1547,1653,

%T 1759,1861,1967,2071,2173,2279,2383,2489,2597,26101,27103,28107,29109,

%U 30113,31127,32131,33137,34139,35149,36151,37157,38163,39167,40173,41179,42181

%N Concatenate n with n-th prime.

%C Triangular numbers are 1653, 32131, 79401, ... - _Ali Adams_, Feb 04 2020

%C The next such terms are 173340627863131 and 1454987833022905581. - _Giovanni Resta_, Feb 04 2020

%H Reinhard Zumkeller, <a href="/A045532/b045532.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n*10^(A004216(A000040(n))+1) + A000040(n). - _Reinhard Zumkeller_, Sep 03 2002

%t Table[FromDigits[Join[IntegerDigits[n], IntegerDigits[Prime[n]]]], {n, 40}] (* _Vincenzo Librandi_, Apr 13 2019 *)

%t #[[1]]*10^IntegerLength[#[[2]]]+#[[2]]&/@Table[{n,Prime[n]},{n,50}] (* _Harvey P. Dale_, Oct 11 2024 *)

%o (Haskell)

%o a045532 n = read $ show n ++ show (a000040 n) :: Integer

%o -- _Reinhard Zumkeller_, Jul 08 2014

%o (Magma) [Seqint(Intseq(NthPrime(n)) cat Intseq(n)): n in [1..45]]; // _Vincenzo Librandi_, Apr 13 2019

%o (PARI) a(n) = eval(Str(n,prime(n))); \\ _Michel Marcus_, Apr 13 2019, simplified by _M. F. Hasler_, Feb 05 2020

%o (Python)

%o from sympy import prime

%o def a(n): return int(str(n) + str(prime(n)))

%o print([a(n) for n in range(1, 43)]) # _Michael S. Branicky_, Dec 23 2021

%Y Cf. A000040, A075110.

%Y Cf. A085451. [_Reinhard Zumkeller_, Jun 30 2010]

%K nonn,base

%O 1,1

%A _Jeff Burch_