A134468 Numbers n such that 2^n and 3^n have the same leading digit.

0, 17, 28, 34, 40, 51, 57, 68, 80, 84, 85, 91, 97, 103, 107, 108, 114, 120, 125, 130, 142, 143, 147, 154, 159, 170, 176, 182, 187, 193, 199, 204, 206, 210, 216, 227, 233, 244, 250, 256, 260, 261, 267, 273, 278, 283, 284, 296, 301, 307, 318, 319, 323, 324, 330

Offset: 1

Author

Lekraj Beedassy, Jan 20 2008

Keywords

• nonn
• base

Crossrefs

Cf. A008952, A060956.

Programs

Maple

A000030 := proc(n) op(-1, convert(n,base,10)) ; end: isA134468 := proc(n) if A000030(2^n) = A000030(3^n) then true ; else false; fi ; end: for n from 0 to 800 do if isA134468(n) then printf("%d, ",n) ; fi ; od: # R. J. Mathar, Jan 30 2008

Mathematica

Select[Range[0, 500], IntegerDigits[2^# ][[1]] == IntegerDigits[3^# ][[1]] &] (* Stefan Steinerberger, Jan 21 2008 *)

Extensions

More terms from Stefan Steinerberger, Jan 21 2008

More terms from R. J. Mathar, Jan 30 2008