A154111 -id:A154111 - cp's OEIS frontend

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

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, 70, 72, 74, 75, 77, 79, 81, 89, 90, 95, 96, 97, 100, 101, 104, 105, 111, 114, 115, 121, 126, 131, 136, 145, 151, 154, 156, 161, 171, 174, 175, 180, 182, 191, 199, 200, 202, 207

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 04 2009

			2^3-1^2 = 7, 3^3-2^2 = 23, ...

G. C. Greubel, Table of n, a(n) for n = 1..2000

Cf. A140719, A005097, A154111.

[n: n in [0..5000] | IsPrime(((n+1)^3-n^2))]; // Vincenzo Librandi, Nov 26 2010

a[n_]:=(n+1)^3-n^2;lst={};Do[If[PrimeQ[a[n]],AppendTo[lst,n]],{n,6!}];lst
Select[Range[210],PrimeQ[(#+1)^3-#^2]&] (* Harvey P. Dale, Sep 20 2011 *)

is(n)=isprime((n+1)^3 - n^2) \\ Charles R Greathouse IV, Sep 02 2016

A154113 Primes of the form (n+1)^3 - n^2.

Original entry on oeis.org

7, 23, 109, 191, 307, 463, 919, 1231, 1607, 2053, 4657, 7639, 8861, 34913, 41719, 53503, 77743, 89189, 95311, 122599, 138007, 146173, 182057, 223381, 246203, 353011, 383833, 416399, 433351, 468623, 505759, 544807, 721079, 745471, 875711

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 04 2009

			2^3-1^2=7, 3^3-2^2=23, ...

G. C. Greubel, Table of n, a(n) for n = 1..2000

Cf. A140719, A005097, A154111, A154112.

[a: n in [0..100] | IsPrime(a) where a is (n+1)^3 - n^2]; // Vincenzo Librandi, Sep 02 2016

a[n_]:=(n+1)^3-n^2;lst={};Do[If[PrimeQ[a[n]],AppendTo[lst,a[n]]],{n,6!}];lst
Select[(#+1)^3-#^2&/@Range[200],PrimeQ]  (* Harvey P. Dale, Mar 14 2011 *)

for(n=1,1e3, if(isprime(t=(n+1)^3 - n^2), print1(t", "))) \\ Charles R Greathouse IV, Sep 02 2016

A154115 Numbers n such that n + 3 is prime.

Original entry on oeis.org

0, 2, 4, 8, 10, 14, 16, 20, 26, 28, 34, 38, 40, 44, 50, 56, 58, 64, 68, 70, 76, 80, 86, 94, 98, 100, 104, 106, 110, 124, 128, 134, 136, 146, 148, 154, 160, 164, 170, 176, 178, 188, 190, 194, 196, 208, 220, 224, 226, 230, 236, 238, 248, 254, 260, 266, 268, 274, 278

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 04 2009

			a(2) = 2 since (2 + 2)^2 - (2 + 1)^2 - 2 = 5.

G. C. Greubel, Table of n, a(n) for n = 1..2000

Cf. A140719, A005097, A154111, A154112, A154113.

Cf. A067076 (a(n-1)/2).

[n: n in [0..500] | IsPrime((n+2)^2-(n+1)^2-n)]; // Vincenzo Librandi, Nov 26 2010

A154115 := proc(n) ithprime(n+1)-3 ; end proc: # R. J. Mathar, May 09 2010

a[n_]:=(n+2)^2-(n+1)^2-n;lst={};Do[If[PrimeQ[a[n]],AppendTo[lst,n]],{n,6!}];lst
Select[Range[0,300],PrimeQ[(#+2)^2-(#+1)^2-#]&] (* Harvey P. Dale, Nov 06 2013 *)
Prime[Range[2,100]]-3 (* Harvey P. Dale, Jul 15 2017 *)

is(n)=isprime(n+3) \\ Charles R Greathouse IV, Sep 02 2016

a(n) = A086801(n+1). - R. J. Mathar, May 09 2010

New name based on a comment by Franklin T. Adams-Watters, Jan 30 2009

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

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A154113 Primes of the form (n+1)^3 - n^2.

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A154115 Numbers n such that n + 3 is prime.

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