A378000
Array read by ascending antidiagonals: T(n,k) is the k-th positive integer that is digitally balanced in base n.
Original entry on oeis.org
2, 11, 9, 75, 15, 10, 694, 78, 19, 12, 8345, 698, 99, 21, 35, 123717, 8350, 714, 108, 260, 37, 2177399, 123723, 8375, 722, 114, 266, 38, 44317196, 2177406, 123759, 8385, 738, 120, 268, 41, 1023456789, 44317204, 2177455, 123771, 8410, 742, 135, 278, 42
Offset: 2
Array begins:
n\k| 1 2 3 4 5 ...
-------------------------------------------------------------------------
2 | 2, 9, 10, 12, 35, ... = A031443
3 | 11, 15, 19, 21, 260, ... = A049354
4 | 75, 78, 99, 108, 114, ... = A049355
5 | 694, 698, 714, 722, 738, ... = A049356
6 | 8345, 8350, 8375, 8385, 8410, ... = A049357
7 | 123717, 123723, 123759, 123771, 123807, ... = A049358
8 | 2177399, 2177406, 2177455, 2177469, 2177518, ... = A049359
9 | 44317196, 44317204, 44317268, 44317284, 44317348, ... = A049360
10 | 1023456789, 1023456798, 1023456879, 1023456897, 1023456978, ...
11 | 26432593615, 26432593625, 26432593725, 26432593745, 26432593845, ...
... | \______ A378001 (main diagonal)
A049363
T(2,4) = 12 = 1100_2 is the fourth number in base 2 containing an equal amount of zeros and ones.
T(9,5) = 44317348 = 102345867_9 is the fifth number in base 9 containing an equal amount of digits from 0 to 8.
-
Module[{dmax = 10, a, m}, a = Table[m = FromDigits[Join[{1, 0}, Range[2, n-1]], n] - 1; Table[While[!SameQ@@DigitCount[++m, n]]; m, dmax-n+2], {n, dmax+1, 2, -1}]; Array[Diagonal[a, # - dmax] &, dmax]]
A145100
Integers in which no more than half the digits (rounded up) are the same, for all bases up to ten.
Original entry on oeis.org
1, 2, 17, 19, 25, 38, 52, 56, 75, 76, 82, 83, 90, 92, 97, 98, 100, 102, 104, 105, 108, 113, 116, 135, 139, 141, 142, 147, 150, 153, 163, 165, 177, 178, 180, 184, 195, 197, 198, 201, 204, 209, 210, 212, 225, 226, 232, 267, 269, 275, 278, 279, 291, 293, 294, 298
Offset: 1
267 in bases [2, 10] is 100001011, 100220, 10023, 2032, 1123, 531, 413, 326, 267. There are five zeros out of nine digits in its binary representation and no more than half the digits in the other bases are identical.
Cf.
A049354,
A049355,
A049356,
A049357,
A049358,
A049359,
A049360,
A049361,
A049362,
A049363,
A049364
A031947
Numbers in which 0,1,2,3,4,5 all occur in base 6.
Original entry on oeis.org
8345, 8350, 8375, 8385, 8410, 8415, 8525, 8530, 8585, 8600, 8620, 8630, 8735, 8745, 8765, 8780, 8835, 8840, 8950, 8955, 8980, 8990, 9015, 9020, 10505, 10510, 10535, 10545, 10570, 10575, 11045, 11050, 11165, 11190, 11200, 11220, 11255, 11265, 11345, 11370, 11415
Offset: 1
-
isA031947 := proc(n)
convert(convert(n,base,6),set) ;
if nops(%) = 6 then
true;
else
false;
end if;
end proc:
for n from 1 to 12000 do
if isA031947(n) then
print(n);
end if;
end do: # R. J. Mathar, Aug 24 2023
A145101
Integers in which no digit occurs more than once more often than any other digit and not all repeated digits are identical, for all bases up to ten.
Original entry on oeis.org
1, 2, 17, 19, 25, 38, 52, 56, 75, 76, 82, 90, 92, 98, 100, 102, 104, 105, 108, 116, 141, 142, 150, 153, 177, 178, 180, 184, 195, 198, 204, 210, 212, 225, 226, 232, 294, 308, 316, 332, 395, 396, 410, 412, 420, 434, 450, 460, 481, 542, 572, 611, 689, 752, 818
Offset: 1
97 is in A145100 but not in this sequence: in base 3 it is 10121 and 1 occurs two times more often than either 0 or 2.
98 is in this sequence: in bases [2, 10] it is 1100010, 10122, 1202, 343, 242, 200, 142, 118, 98.
Cf.
A049354,
A049355,
A049356,
A049357,
A049358,
A049359,
A049360,
A049361,
A049362,
A049363,
A049364,
A145100
A145104
Digitally fair numbers: integers n such that in all bases b = 2..10 no digit occurs more often than ceiling(d/b) times, where d is the number of digits of n in base b.
Original entry on oeis.org
1, 2, 19, 198, 25410896, 31596420, 10601629982, 10753657942, 11264883970, 11543640378, 11553029646, 11665278790, 12034384190, 12038440382, 12366849814, 12519032774, 12781964290, 12971872086, 13156400486
Offset: 1
Cf.
A049354,
A049355,
A049356,
A049357,
A049358,
A049359,
A049360,
A049361,
A049362,
A049363,
A049364,
A145100,
A145101.
Showing 1-5 of 5 results.
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