A122955 - OEIS

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.

%I #8 Jan 21 2022 23:30:46

%S 5,11,12,13,19,25,28,29,33,35,45,46,52,53,58,59,61,62,63,65,76,78,79,

%T 81,85,88,89,91,92,95,98,101,104,108,109,114,115,116,119,125,131,136,

%U 139,144,145,158,161,162,168,169,178,179,181,184,185,189,195,197,199,207

%N 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.

%C Conjecture: Natural density is log 5/log 100. - _Charles R Greathouse IV_, Nov 15 2010

%e 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.

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

%Y Cf. A066001.

%K nonn,base

%O 1,1

%A _Robert G. Wilson v_, Oct 25 2006