A240580 Numbers k such that DigitSum(5^k) > DigitSum(5^(k+1)).
4, 10, 11, 12, 16, 18, 24, 27, 28, 32, 34, 36, 39, 44, 45, 49, 51, 52, 57, 58, 60, 61, 62, 63, 64, 69, 75, 76, 77, 78, 80, 83, 84, 87, 88, 90, 91, 94, 96, 97, 100, 103, 106, 107, 108, 113, 114, 115, 118, 119, 124, 129, 130, 132, 135, 138, 139, 142, 143, 144, 149
Offset: 1
Examples
The digitsum(5^4) = 13 > 11 = digitsum(5^(4+1)). Hence, 4 appears in the sequence. The digitsum(5^11) = 38 > 28 = digitsum(5^(11+1)). Hence, 11 appears in the sequence.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..1000
Crossrefs
Programs
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Maple
a := proc(n) local a,b,d,e; a:=5^n; b:=add( i,i = convert((a), base, 10))(a); d:=5^(n+1); e:=add( i,i = convert((d), base, 10))(d); if b > e then RETURN (n); fi; end: seq(a(n), n=1..300);
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Mathematica
k=Table[Total[IntegerDigits[5^n,10]],{n,1,300}];Flatten[Position[Greater@@@Partition[k,2,1],True]] Select[Range[150],Total[IntegerDigits[5^#]]>Total[IntegerDigits[5^(#+1)]]&] (* Harvey P. Dale, Jun 04 2025 *)