A018802 Smallest power of 2 that begins with n.

1, 2, 32, 4, 512, 64, 70368744177664, 8, 9007199254740992, 1024, 1125899906842624, 128, 131072, 140737488355328, 151115727451828646838272, 16, 17179869184, 18014398509481984, 19342813113834066795298816, 2048, 2147483648

Offset

1,2

References

A. M. Yaglom and I. M. Yaglom, Challenging Mathematical Problems With Elementary Solutions, Vol. 1 pp. 29, 199-200; Prob. 91a, Dover NY 1987

Links

Christian N. K. Anderson, Table of n, a(n) for n = 1..981 (a(982) has 1196 digits)

Formula

a(n) = 2^A018856(n). - Seiichi Manyama, Jan 29 2017

a(2^n) = 2^n for n >= 0. - Seiichi Manyama, Jan 29 2017

Example

a(7) = 70368744177664, because 2^46 is the smallest power of 2 that begins with a 7.

Prog

(R) library(gmp); ndig<-function(i) nchar(as.character(as.bigz(i))) y=as.bigz(rep(0, 100)); for(i in 1:100) {n=as.bigz(2); while(substr(n, 1, ndig(i))!=as.character(i)) n=n*2; y[i]=n; } # Christian N. K. Anderson, May 23 2013

Crossrefs

Cf. A018856.

Cf. this sequence (k=2), A018857 (k=3), A018859 (k=4), A018861 (k=5), A018863 (k=6), A018865 (k=7), A018867 (k=8), A018869 (k=9).

Sequence in context: A247873 A281901 A357176 * A166487 A004842 A022378

Adjacent sequences: A018799 A018800 A018801 * A018803 A018804 A018805

Keyword

nonn,base

Author

David W. Wilson

Status

approved