

A172027


a(1) = 1; for n > 1, a(n) = smallest k such that a(n1)^3 + k is a cube.


2




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 bfile. a(12) has 1386 digits and is too large to include in the bfile.  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(n1)*(a(n1) + 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(n1)*(Self(n1)+1): n in [1..8] ]; // Klaus Brockhaus, Mar 16 2010


CROSSREFS

Cf. A172028.
Sequence in context: A012067 A012145 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



