cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A031994 Duplicate of A023751.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43
Offset: 1

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Keywords

A329299 Numbers whose digits are in nondecreasing order in bases 9 and 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 22, 23, 24, 25, 26, 33, 34, 35, 44, 111, 112, 113, 114, 115, 116, 122, 123, 124, 125, 133, 134, 188, 222, 223, 224, 233, 277, 278, 366, 367, 368, 377, 455, 456, 457, 458, 466, 467, 556, 557, 566, 1113
Offset: 1

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Author

Jon E. Schoenfield, Nov 17 2019

Keywords

Comments

a(91) = 12555566 is the largest term < 10^10000 (which is a 10480-digit number in base 9). But can it be proved that 12555566 is the final term of the sequence?

Examples

			Sequence includes, respectively, 9, 16, 32, and 11 terms that are 1-, 2-, 3-, and 4- digit terms in both bases, and the following:
  a(69) =    14777 =    22238_9
  a(70) =    15677 =    23448_9
  a(71) =    22234 =    33444_9
  a(72) =    22235 =    33445_9
  a(73) =    22236 =    33446_9
  a(74) =    22237 =    33447_9
  a(75) =    22238 =    33448_9
  a(76) =    22244 =    33455_9
  a(77) =    22245 =    33456_9
  a(78) =    22246 =    33457_9
  a(79) =    22247 =    33458_9
  a(80) =    22255 =    33467_9
  a(81) =    22256 =    33468_9
  a(82) =    22335 =    33566_9
  a(83) =    22336 =    33567_9
  a(84) =    22337 =    33568_9
  a(85) =    22345 =    33577_9
  a(86) =    22346 =    33578_9
  a(87) =    22355 =    33588_9
  a(88) =    44468 =    66888_9
  a(89) =   222344 =   367888_9
  a(90) =  1233467 =  2278888_9
  a(91) = 12555566 = 25555888_9
		

Crossrefs

Intersection of A023751 (base 9) and A009994 (base 10). Numbers whose digits are in nondecreasing order in bases b and b+1: A329294 (b=4), A329295 (b=5), A329296 (b=6), A329297 (b=7), A329299 (b=8), this sequence (b=9). See A329300 for the (apparently) largest term of each of these sequences.

Programs

  • Maple
    filter:= proc(n) local L;
      L:= convert(n,base,10);
      `and`(seq(L[i+1]<=L[i],i=1..nops(L)-1))
    end proc:
    ND[1]:= [$1..8]: R:= $0..8:
    for d from 2 to 10 do
      ND[d]:= map(t -> seq(9*t+r, r=(t mod 9) ..8), ND[d-1]);
      R:= R, op(select(filter, ND[d]));
    od:
    R; # Robert Israel, Nov 20 2019
  • Mathematica
    Select[Range[0,1200],Min[Differences[IntegerDigits[#]]]>-1&& Min[ Differences[ IntegerDigits[ #,9]]]>-1&] (* Harvey P. Dale, Oct 14 2022 *)

A329298 Numbers whose digits are in nondecreasing order in bases 8 and 9.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 30, 31, 91, 92, 93, 94, 95, 101, 102, 103, 111, 151, 182, 183, 222, 223, 293, 294, 295, 303, 365, 366, 367, 374, 375, 822, 823, 831, 951, 1023, 10023, 14774, 14775, 14783, 599551, 608623, 1203126, 1203127, 1203135
Offset: 1

Views

Author

Jon E. Schoenfield, Nov 17 2019

Keywords

Comments

There are no more terms through 10^10000 (which is an 11074-digit number in base 8 and a 10480-digit number in base 9). But can it be proved that 1203135 is the final term of the sequence?

Examples

			Sequence includes 8 terms that are 1-digit numbers in both bases, 12 that are 2-digit numbers in both bases, 23 that are 3-digit terms in both bases, and the following:
  a(44) =     822 =    1466_8 =    1113_9
  a(45) =     823 =    1467_8 =    1114_9
  a(46) =     831 =    1477_8 =    1123_9
  a(47) =     951 =    1667_8 =    1266_9
  a(48) =    1023 =    1777_8 =    1356_9
  a(49) =   10023 =   23447_8 =   14666_9
  a(50) =   14774 =   34666_8 =   22235_9
  a(51) =   14775 =   34667_8 =   22236_9
  a(52) =   14783 =   34677_8 =   22245_9
  a(53) =  599551 = 2222777_8 = 1113377_9
  a(54) =  608623 = 2244557_8 = 1126777_9
  a(55) = 1203126 = 4455666_8 = 2233336_9
  a(56) = 1203127 = 4455667_8 = 2233337_9
  a(57) = 1203135 = 4455677_8 = 2233346_9
		

Crossrefs

Intersection of A023750 (base 8) and A023751 (base 9). Numbers whose digits are in nondecreasing order in bases b and b+1: A329294 (b=4), A329295 (b=5), A329296 (b=6), A329297 (b=7), this sequence (b=8), A329299 (b=9). See A329300 for the (apparently) largest term of each of these sequences.

A032856 Numbers whose base-9 representation Sum_{i=0..m} d(i)*9^i has d(m) <= d(m-1) >= d(m-2) <= ...

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 50, 51, 52, 53, 60, 61, 62, 70, 71, 80, 90, 91, 99, 100, 101, 108, 109, 110, 111, 117, 118, 119, 120, 121, 126
Offset: 1

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Keywords

Crossrefs

Cf. A023751 (subsequence).
Showing 1-4 of 4 results.