A025708 - OEIS

%I #18 Nov 13 2025 02:27:59

%S 1,2,4,7,11,16,21,27,34,42,51,61,71,82,94,107,121,136,151,167,184,202,

%T 221,241,261,282,304,327,351,375,400,426,453,481,510,539,569,600,632,

%U 665,699,733,768,804,841,879,918,957,997,1038,1080,1123,1167,1211,1256,1302

%N Index of 5^n within the sequence of the numbers of the form 5^i*7^j.

%C Position of zeros in A025667. - _R. J. Mathar_, Jul 06 2025

%H Charles R Greathouse IV, <a href="/A025708/b025708.txt">Table of n, a(n) for n = 0..10000</a>

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

%F A003595(a(n)) = 5^n.

%F a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_7(5) (A153203).

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

%t Accumulate[Table[Ceiling[n * Log[7, 5]], {n, 0, 60}]] + 1 (* _Amiram Eldar_, Nov 13 2025 *)

%o (PARI) a(n)=my(N=1); n+1+sum(i=1, n, logint(N*=5, 7)); \\ _Charles R Greathouse IV_, Jan 11 2018

%o (PARI) first(n)=my(s, N=1/5); vector(n+1, i, s+=logint(N*=5, 7)+1) \\ _Charles R Greathouse IV_, Jan 11 2018

%Y Cf. A000351, A003595, A025667, A153203.

%K nonn,easy

%O 0,2

%A _David W. Wilson_

%E Offset corrected by _Charles R Greathouse IV_, Jan 11 2018