A172027 a(1) = 1; for n > 1, a(n) = smallest k such that a(n-1)^3 + k is a cube.

1, 7, 169, 86191, 22286924017, 1490120946485455020919, 6661381305464124918785090511089856547876441

Offset

1,2

Comments

a(8) has 87 decimal digits.

A subsequence of A003215 (centered hexagonal numbers: 3n(n+1)+1, also first differences of A000578). - Klaus Brockhaus, Mar 20 2010

a(11) has 693 digits and is the last term in the b-file. a(12) has 1386 digits and is too large to include in the b-file. - Harvey P. Dale, Jul 31 2019

Links

Harvey P. Dale, Table of n, a(n) for n = 1..11

Formula

a(n) = 1 + 3*a(n-1)*(a(n-1) + 1). - Zak Seidov, Jun 25 2010

Example

n = 2: for k = 7, a(1)^3+k = 1^3+7 = 9 = 2^3 is a cube; 7 is the smallest such k, therefore a(2) = 7.
n = 4: for k = 86191, a(3)^3+k = 169^3+86191 = 4913000 = 170^3 is a cube; 86191 is the smallest such k, therefore a(4) = 86191.

Mathematica

NestList[3#^2+3#+1&, 1, 6] (* Harvey P. Dale, Jul 31 2019 *)

Prog

(Magma) /* inefficient, uses definition */ a:=1; S:=[a]; for n in [2..4] do k:=0; flag:= true; while flag do k+:=1; if IsPower(a^3+k, 3) then Append(~S, k); a:=k; flag:=false; end if; end while; end for; S;
/* uses formula from R. J. Mathar, see A172028 */ [ n eq 1 select 1 else 1+3*Self(n-1)*(Self(n-1)+1): n in [1..8] ]; // Klaus Brockhaus, Mar 16 2010

Crossrefs

Cf. A172028.

Sequence in context: A368839 A351154 A005019 * A113562 A157203 A178019

Adjacent sequences: A172024 A172025 A172026 * A172028 A172029 A172030

Keyword

nonn

Author

Vincenzo Librandi, Jan 23 2010

Extensions

Edited and a(7) added by Klaus Brockhaus, Mar 16 2010

Status

approved