A172029 a(1) = 3; for n > 1, a(n) = smallest k such that a(n-1)^3 + k is a cube.

3, 37, 4219, 53412541, 8558698768467667, 219753973828109905009157978671669, 144875427039736839295788447509321763094522140738437260379045751691

Offset

1,1

Comments

a(8) has 131 decimal digits.

From a(2) onward a subsequence of A003215 (centered hexagonal numbers: 3n(n+1)+1, also first differences of A000578). - Klaus Brockhaus, Mar 20 2010

Links

Table of n, a(n) for n=1..7.

Example

n = 2: for k = 37, a(1)^3+k = 3^3+37 = 64 = 4^3 is a cube; 37 is the smallest such k, therefore a(2) = 37.
n = 4: for k = 53412541, a(3)^3+k = 4219^3+53412541 = 75151448000 = 4220^3 is a cube; 53412541 is the smallest such k, therefore a(4) = 53412541.

Prog

(Magma) /* inefficient, uses definition */ a:=3; 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 3 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: A261594 A351759 A132931 * A120480 A088098 A284411

Adjacent sequences: A172026 A172027 A172028 * A172030 A172031 A172032

Keyword

nonn

Author

Vincenzo Librandi, Jan 23 2010

Extensions

Edited, a(4), a(5) corrected and a(6), a(7) added by Klaus Brockhaus, Mar 16 2010

Status

approved