A215830 Numbers k such that 2^k contains each decimal digit at least twice.

88, 104, 113, 114, 116, 117, 118, 119, 120, 125, 126, 131, 133, 134, 136, 140, 141, 142, 144, 145, 146, 147, 148, 150, 155, 156, 157, 159, 160, 161, 162, 163, 164, 165, 166, 170, 171, 172, 175, 177, 178, 179, 180, 181, 182, 185, 186, 187, 188, 189, 190, 191, 192

Offset

1,1

Comments

A subsequence of A130694.

Motivated by J. Merickel's question about the least power of 2 in which all digits 0-9 occur a prime number of times. The first 4 terms of this sequence are all such that this is the case for all but one digit; see Examples.

Beyond 184, the numbers 195-197 and 229 are the only exponents < 10^4 which are not in this sequence. Is 229 the largest such number?

Links

Table of n, a(n) for n=1..53.

J. Merickel, Are these new questions?, Yahoo! group "primenumbers", Aug 24 2012.

James Merickel, Are these new questions?, message 24399 in primenumbers Yahoo group, Aug 24, 2012.

Example

Digit counts for 2^n:
.
  n\d| 0  1  2  3  4  5  6  7  8  9
  ---+-----------------------------
   88| 5  2  2  2  3  3  2  2  4* 2
  104| 5  3  6* 2  3  2  5  2  2  2
  113| 5  3  3  2  3  5  4* 3  2  5
  114| 3  7  2  5  4* 2  2  2  5  3
.
*nonprime counts

Prog

(PARI) is_A215830(n)={my(c=vector(10), N=[1<<n, 0]); while(N=divrem(N[1], 10), c[N[2]+1]++); vecmin(c)>1}

Crossrefs

Sequence in context: A241491 A356368 A068356 * A216873 A114166 A350324

Adjacent sequences: A215827 A215828 A215829 * A215831 A215832 A215833

Keyword

nonn,base

Author

M. F. Hasler, Aug 25 2012

Status

approved