A381837 -id:A381837 - cp's OEIS frontend

A381836 k/25 is in this list if A053824(k) < A112765(k), i.e. if digitsum(k, 5) < valuation(k, 5).

1, 5, 10, 25, 30, 50, 75, 125, 130, 150, 175, 250, 275, 375, 500, 625, 630, 650, 675, 750, 775, 875, 1000, 1250, 1275, 1375, 1500, 1875, 2000, 2500, 3125, 3130, 3150, 3175, 3250, 3275, 3375, 3500, 3750, 3775, 3875, 4000, 4375, 4500, 5000, 5625, 6250, 6275, 6375

Offset: 1

Peter Luschny, Mar 08 2025

Cf. A053824, A112765.

Cf. A371176 (base 2), A381838 (base 3), A381837 (base 4).

aList := upto -> local k; [seq(k/25, k in select(n -> add(convert(n, base, 5)) < padic[ordp](n, 5), [seq(25..upto,25)]))]: aList(160000);

Select[Range[160000],DigitSum[#,5]Stefano Spezia, Mar 08 2025 *)

def aList(upto, b): return [n/b^2 for n in srange(b^2, upto, b^2) if sum(n.digits(b)) < valuation(n, b)]
print(aList(160000, 5))

A381838 k/9 is in this list if A053735(k) < A007949(k), i.e. if digitsum(k, 3) < valuation(k, 3).

Original entry on oeis.org

1, 3, 6, 9, 12, 18, 27, 30, 36, 45, 54, 63, 81, 84, 90, 99, 108, 117, 135, 162, 171, 189, 216, 243, 246, 252, 261, 270, 279, 297, 324, 333, 351, 378, 405, 432, 486, 495, 513, 540, 567, 594, 648, 729, 732, 738, 747, 756, 765, 783, 810, 819, 837, 864, 891, 918, 972, 981, 999

Offset: 1

Peter Luschny, Mar 08 2025

Cf. A007949, A053735.

Cf. A371176 (base 2), A381837 (base 4), A381836 (base 5).

aList := upto -> local k; [seq(k/9, k in select(n -> add(convert(n, base, 3)) < padic[ordp](n, 3), [seq(9..upto,9)]))]: aList(9000);

Select[Range[9000],DigitSum[#,3]Stefano Spezia, Mar 08 2025 *)

def aList(upto, b): return [n/b^2 for n in srange(b^2, upto, b^2) if sum(n.digits(b)) < valuation(n, b)]
print(aList(9000, 3))

A381834 k/16 is in this list if k > 4 and A053737(k) = A235127(k), i.e. if digitsum(k, 4) = valuation(k, 4).

Original entry on oeis.org

2, 5, 12, 17, 24, 36, 65, 72, 84, 112, 132, 160, 208, 257, 264, 276, 304, 324, 352, 400, 516, 544, 592, 704, 784, 896, 1025, 1032, 1044, 1072, 1092, 1120, 1168, 1284, 1312, 1360, 1472, 1552, 1664, 1856, 2052, 2080, 2128, 2240, 2320, 2432, 2624, 3088, 3200, 3392

Offset: 1

Peter Luschny, Mar 09 2025

Cf. A053737, A235127, A381837.

Cf. A381835 (base = 3), A381833 (base = 5).

Select[Range[16, 60000, 16], DigitSum[#, 4] == IntegerExponent[#, 4] &] / 16

cp's OEIS Frontend

A381836 k/25 is in this list if A053824(k) < A112765(k), i.e. if digitsum(k, 5) < valuation(k, 5).

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A381838 k/9 is in this list if A053735(k) < A007949(k), i.e. if digitsum(k, 3) < valuation(k, 3).

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

SageMath

A381834 k/16 is in this list if k > 4 and A053737(k) = A235127(k), i.e. if digitsum(k, 4) = valuation(k, 4).

Views

Author

Keywords

Crossrefs

Programs

Mathematica