A159078 Number of perfect powers with distinct digits in base n.

1, 1, 9, 8, 25, 50, 88, 297, 657, 1418, 3212, 8662, 24185, 64103, 183718

Offset

2,3

Links

Table of n, a(n) for n=2..16.

Example

The 8 powers with unique digits in base 5 are 1, 4, 8, 9, 16, 27, 144, and 576; in base 5 these are 1, 4, 13, 14, 31, 102, 1304, and 4301.

Prog

(PARI) okdigs(digs) = {for (i = 1, #digs-1, for (j = i+1, #digs, if (digs[j] == digs[i], return (0); ); ); ); return (1); }
a(n) = {b = n; sols = Set([1]); vmax = b^b; pmax = ceil(log(vmax)/log(2)); for (p = 2, pmax, i = 2; while ((iep = i^p) < vmax, if (okdigs(digits(iep, b)), sols = Set(concat(sols, iep)); ); i++; ); ); #sols; } \\ Michel Marcus, Aug 19 2013

Crossrefs

Cf. A075309

Sequence in context: A068823 A264301 A251091 * A253090 A154226 A177187

Adjacent sequences: A159075 A159076 A159077 * A159079 A159080 A159081

Keyword

nonn,base,more

Author

Johan Särnbratt, Apr 04 2009

Extensions

a(11) - a(16) from Johan Särnbratt, Apr 21 2009

Status

approved