A025713 - OEIS

%I #13 Nov 13 2025 09:42:30

%S 1,3,7,12,19,28,38,50,64,79,96,114,134,156,179,204,231,259,289,320,

%T 353,388,424,462,502,543,586,631,677,725,774,825,878,932,988,1046,

%U 1105,1166,1228,1292,1358,1425,1494,1565,1637,1711,1787,1864,1943,2023,2105,2189

%N Index of 6^n within the sequence of the numbers of the form 3^i*6^j.

%C Positions of zeros in A025641. - _R. J. Mathar_, Jul 06 2025

%H Amiram Eldar, <a href="/A025713/b025713.txt">Table of n, a(n) for n = 0..10000</a>

%F From _Amiram Eldar_, Nov 13 2025: (Start)

%F A025614(a(n)) = 6^n.

%F a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_3(6) (A153459).

%F a(n) ~ c * n^2 / 2, where c is defined above. (End)

%t Accumulate[Table[Ceiling[n * Log[3, 6]], {n, 0, 60}]] + 1 (* _Amiram Eldar_, Nov 13 2025 *)

%Y Cf. A000400, A025614, A025641, A153459.

%K nonn,easy

%O 0,2

%A _David W. Wilson_

%E Offset corrected by _Amiram Eldar_, Nov 13 2025