cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A014683 In the sequence of positive integers add 1 to each prime number.

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%I A014683 #27 Jun 22 2025 12:57:06
%S A014683 1,3,4,4,6,6,8,8,9,10,12,12,14,14,15,16,18,18,20,20,21,22,24,24,25,26,
%T A014683 27,28,30,30,32,32,33,34,35,36,38,38,39,40,42,42,44,44,45,46,48,48,49,
%U A014683 50,51,52,54,54,55,56,57,58,60,60,62,62,63,64,65,66,68,68,69,70,72,72
%N A014683 In the sequence of positive integers add 1 to each prime number.
%C A014683 For n >= 3, a(n) = smallest composite number m such that m - (n-2) is a prime. - _Amarnath Murthy_ and Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Mar 08 2003
%C A014683 Möbius transform of sigma(n)+omega(n) = A380457(n). - _Wesley Ivan Hurt_, Jun 22 2025
%H A014683 N. J. A. Sloane, <a href="/A014683/b014683.txt">Table of n, a(n) for n = 1..10000</a>
%F A014683 a(n) = n + pi(n) - pi(n-1). - _Wesley Ivan Hurt_, Jun 15 2013
%F A014683 a(n) = n + A010051(n). - _Reinhard Zumkeller_, Nov 01 2014
%F A014683 a(n) = Sum_{d|n} A380457(d)*mu(n/d). - _Wesley Ivan Hurt_, Jun 22 2025
%t A014683 Array[If[PrimeQ[#],#+1,#]&,80] (* _Harvey P. Dale_, Jul 21 2013 *)
%o A014683 (PARI) a(n)=n+isprime(n)
%o A014683 (Haskell)
%o A014683 a014683 n = n + a010051' n  -- _Reinhard Zumkeller_, Nov 01 2014
%o A014683 (Python)
%o A014683 from sympy import isprime
%o A014683 def A014683(n): return n+isprime(n) # _Chai Wah Wu_, Oct 03 2024
%Y A014683 Cf. A010051, A113646, A380457.
%K A014683 nonn,easy
%O A014683 1,2
%A A014683 _Mohammad K. Azarian_
%E A014683 More terms from _Erich Friedman_.