A122955 Numbers k such that although the number of digits in 5^k is larger, the sum of the digits is less than that of the previous power of 5.

5, 11, 12, 13, 19, 25, 28, 29, 33, 35, 45, 46, 52, 53, 58, 59, 61, 62, 63, 65, 76, 78, 79, 81, 85, 88, 89, 91, 92, 95, 98, 101, 104, 108, 109, 114, 115, 116, 119, 125, 131, 136, 139, 144, 145, 158, 161, 162, 168, 169, 178, 179, 181, 184, 185, 189, 195, 197, 199, 207

Offset: 1

Author

Robert G. Wilson v, Oct 25 2006

Keywords

• nonn
• base

Comments

Conjecture: Natural density is log 5/log 100. - Charles R Greathouse IV, Nov 15 2010

Examples

			11 is a term because 5^11 = 48828125 has 8 digits and digit sum 4+8+8+2+8+1+2+5 = 38 while 5^10 = 9765625 has 7 digits and digit sum 9+7+6+5+6+2+5 = 40.
		

Crossrefs

Cf. A066001.

Programs

Mathematica

Select[ Range@ 208, Floor[Log[10, 5^# ]] > Floor[Log[10, 5^(# - 1)]] && Plus @@ IntegerDigits[5^# ] < Plus @@ IntegerDigits[5^(# - 1)] &]