A280824 -id:A280824

Search: a280824 -id:a280824

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A280823

Numbers with an odd number of digits and with an odd number of distinct digits.

+10
4

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 102, 103, 104, 105, 106, 107, 108, 109, 111, 120, 123, 124, 125, 126, 127, 128, 129, 130, 132, 134, 135, 136, 137, 138, 139, 140, 142, 143, 145, 146, 147, 148, 149, 150, 152, 153, 154, 156, 157, 158, 159, 160, 162, 163, 164, 165, 167, 168, 169, 170, 172, 173, 174, 175, 176, 178, 179, 180

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Digit

Index entries for 10-automatic sequences.

FORMULA

A000035(A055642(a(n))) = 1.

A000035(A043537(a(n))) = 1.

MATHEMATICA

Select[Range[0, 180], Mod[Length[IntegerDigits[#1]], 2] == 1 && Mod[Length[Union[IntegerDigits[#1]]], 2] == 1 & ]

Join[{0}, Select[Range[200], AllTrue[{IntegerLength[#], Count[DigitCount[#], _?(#>0&)]}, OddQ]&]] (* Harvey P. Dale, Dec 16 2023 *)

CROSSREFS

Cf. A000035, A001633, A043537, A055642, A280824, A280825, A280826.

KEYWORD

nonn,base,easy

AUTHOR

Ilya Gutkovskiy, Jan 08 2017

STATUS

approved

A280825

Numbers with an odd number of digits and with an even number of distinct digits.

+10
3

100, 101, 110, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 131, 133, 141, 144, 151, 155, 161, 166, 171, 177, 181, 188, 191, 199, 200, 202, 211, 212, 220, 221, 223, 224, 225, 226, 227, 228, 229, 232, 233, 242, 244, 252, 255, 262, 266, 272, 277, 282, 288, 292, 299, 300, 303, 311, 313, 322, 323, 330, 331, 332, 334, 335

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..65.

Eric Weisstein's World of Mathematics, Digit

Index entries for 10-automatic sequences.

FORMULA

A000035(A055642(a(n))) = 1.

A000035(A043537(a(n))) = 0.

a(n) = A210666(n) for n < 244.

MATHEMATICA

Select[Range[335], Mod[Length[IntegerDigits[#1]], 2] == 1 && Mod[Length[Union[IntegerDigits[#1]]], 2] == 0 & ]

CROSSREFS

Cf. A000035, A001633, A043537, A055642, A210666, A280823, A280824, A280826.

KEYWORD

nonn,base,easy

AUTHOR

Ilya Gutkovskiy, Jan 08 2017

STATUS

approved

A280826

Numbers with an even number of digits and with an odd number of distinct digits.

+10
3

11, 22, 33, 44, 55, 66, 77, 88, 99, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1030, 1031, 1033, 1040, 1041, 1044, 1050, 1051, 1055, 1060, 1061, 1066, 1070, 1071, 1077, 1080, 1081, 1088, 1090, 1091, 1099, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..57.

Eric Weisstein's World of Mathematics, Digit

Index entries for 10-automatic sequences.

FORMULA

A000035(A055642(a(n))) = 0.

A000035(A043537(a(n))) = 1.

MATHEMATICA

Select[Range[1110], Mod[Length[IntegerDigits[#1]], 2] == 0 && Mod[Length[Union[IntegerDigits[#1]]], 2] == 1 & ]

endQ[n_]:=Module[{idn=IntegerDigits[n]}, EvenQ[Length[idn]]&&OddQ[ Length[ Union[ idn]]]]; Select[Range[1200], endQ] (* Harvey P. Dale, Mar 31 2019 *)

CROSSREFS

Cf. A000035, A001637, A043537, A055642, A280823, A280824, A280825.

KEYWORD

nonn,base,easy

AUTHOR

Ilya Gutkovskiy, Jan 08 2017

STATUS

approved

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