The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A329172 a(n) is the least positive exponent k such that the decimal expansion of 5^k contains n consecutive zeros. 1
 1, 8, 39, 67, 228, 1194, 3375, 10052, 19699, 26563, 26566, 922553 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From David A. Corneth, Nov 07 2019: (Start) Let z(n) be the largest number of consecutive zeros in 5^n. Then we have |z(n+1) - z(n)| <= 1. So we needn't check every k if it's in the sequence. (End) LINKS Table of n, a(n) for n=0..11. O. M. Cain, The Exceptional Selfcondensability of Powers of Five, arXiv:1910.13829 [math.HO], 2019. EXAMPLE 5^1 = 5 is the first power of 5 that has no zero, so a(0) = 1. 5^8 = 390625 is the first power of 5 that has 1 zero, so a(1) = 8. 5^39 = 1818989403545856475830078125 is the first power of 5 that has 2 consecutive zeros, so a(2) = 39. MATHEMATICA Print[1]; zero = {}; Do[zero = zero <> "0"; k = 1; While[StringPosition[ToString[5^k], zero] == {}, k++]; Print[k]; , {n, 1, 10}] (* Vaclav Kotesovec, Nov 07 2019 *) PROG (PARI) isok(k, n) = {my(d = digits(5^k), pz = select(x->(x==0), d)); if (n<=1, return (#pz == n)); if (#pz < n, return (0)); my(c=0, ok=0, kc=0); for (i=1, #d, if (d[i] == 0, ok = 1; if (ok, c++), if (c > kc, kc=c); ok = 0; c = 0); ); kc == n; } a(n) = my(k=1); while (!isok(k, n), k++); k; (PARI) upto(n) = {my(p5 = 5, res = List()); for(i = 1, n, c = qconsecutivezeros(p5); for(j = #res, c, listput(res, i); print1(i", "); ); p5 *= 5 ); res } qconsecutivezeros(n) = { my(d = digits(n), streak = 0, res = 0); for(i = 1, #d, if(d[i] == 0, streak++ , res = max(streak, res); streak = 0 ) ); res } \\ David A. Corneth, Nov 07 2019 CROSSREFS Cf. A000351 (powers of 5), A006889, A052968 (another family of exponents), A195269, A329174. Sequence in context: A007786 A026662 A196074 * A346326 A003353 A209368 Adjacent sequences: A329169 A329170 A329171 * A329173 A329174 A329175 KEYWORD nonn,base,more,hard AUTHOR Michel Marcus, Nov 07 2019 EXTENSIONS a(9)-a(10) from David A. Corneth, Nov 07 2019 a(11) from Vaclav Kotesovec, Nov 08 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 22 10:24 EDT 2024. Contains 372745 sequences. (Running on oeis4.)