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A154112 Numbers k such that (k+1)^3 - k^2 is prime.

%I A154112 #21 Jan 17 2025 19:22:21
%S A154112 1,2,4,5,6,7,9,10,11,12,16,19,20,32,34,37,42,44,45,49,51,52,56,60,62,
%T A154112 70,72,74,75,77,79,81,89,90,95,96,97,100,101,104,105,111,114,115,121,
%U A154112 126,131,136,145,151,154,156,161,171,174,175,180,182,191,199,200,202,207
%N A154112 Numbers k such that (k+1)^3 - k^2 is prime.
%H A154112 G. C. Greubel, <a href="/A154112/b154112.txt">Table of n, a(n) for n = 1..2000</a>
%e A154112 2^3-1^2 = 7, 3^3-2^2 = 23, ...
%t A154112 a[n_]:=(n+1)^3-n^2;lst={};Do[If[PrimeQ[a[n]],AppendTo[lst,n]],{n,6!}];lst
%t A154112 Select[Range[210],PrimeQ[(#+1)^3-#^2]&] (* _Harvey P. Dale_, Sep 20 2011 *)
%o A154112 (Magma) [n: n in [0..5000] | IsPrime(((n+1)^3-n^2))]; // _Vincenzo Librandi_, Nov 26 2010
%o A154112 (PARI) is(n)=isprime((n+1)^3 - n^2) \\ _Charles R Greathouse IV_, Sep 02 2016
%Y A154112 Cf. A140719, A005097, A154111.
%K A154112 nonn,easy
%O A154112 1,2
%A A154112 _Vladimir Joseph Stephan Orlovsky_, Jan 04 2009