A381836 -id:A381836 - cp's OEIS frontend

A381837 k/16 is in this list if A053737(k) < A235127(k), i.e. if digitsum(k, 4) < valuation(k, 4).

1, 4, 8, 16, 20, 32, 48, 64, 68, 80, 96, 128, 144, 192, 256, 260, 272, 288, 320, 336, 384, 448, 512, 528, 576, 640, 768, 832, 1024, 1028, 1040, 1056, 1088, 1104, 1152, 1216, 1280, 1296, 1344, 1408, 1536, 1600, 1792, 2048, 2064, 2112, 2176, 2304, 2368, 2560, 2816

Offset: 1

Peter Luschny, Mar 08 2025

Cf. A053737, A235127.

Cf. A371176 (base 2), A381838 (base 3), A381836 (base 5).

aList := upto -> local k; [seq(k/16, k in select(n -> add(convert(n, base, 4)) < padic[ordp](n, 4), [seq(16..upto,16)]))]: aList(46000);

Select[Range[46000],DigitSum[#,4]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(46000, 4))

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))

A381833 k/25 is in this list if k > 5 and A053824(k) = A112765(k), i.e. if digitsum(k, 5) = valuation(k, 5).

Original entry on oeis.org

2, 6, 15, 26, 35, 55, 100, 126, 135, 155, 200, 255, 300, 400, 626, 635, 655, 700, 755, 800, 900, 1125, 1255, 1300, 1400, 1625, 1900, 2125, 2625, 3126, 3135, 3155, 3200, 3255, 3300, 3400, 3625, 3755, 3800, 3900, 4125, 4400, 4625, 5125, 6255, 6300, 6400, 6625, 6900, 7125

Offset: 1

Peter Luschny, Mar 09 2025

Cf. A053824, A112765, A381836.

Cf. A381835 (base = 3), A381834 (base = 4).

Select[Range[25, 180000, 25], DigitSum[#, 5] == IntegerExponent[#, 5] &] / 25

cp's OEIS Frontend

A381837 k/16 is in this list if A053737(k) < A235127(k), i.e. if digitsum(k, 4) < valuation(k, 4).

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

SageMath

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

A381833 k/25 is in this list if k > 5 and A053824(k) = A112765(k), i.e. if digitsum(k, 5) = valuation(k, 5).

Views

Author

Keywords

Crossrefs

Programs

Mathematica