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

Author

David W. Wilson

Keywords

• nonn
• base

Examples

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

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)

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).

Programs

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

Formula

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

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