A023746 -id:A023746 - cp's OEIS frontend

A031989 Duplicate of A023746.

0, 1, 2, 3, 5, 6, 7, 10, 11, 15, 21, 22, 23, 26, 27, 31, 42, 43, 47, 63, 85, 86, 87, 90, 91, 95, 106, 107, 111, 127, 170, 171, 175, 191, 255, 341, 342, 343, 346, 347, 351, 362, 363, 367, 383, 426, 427, 431, 447, 511, 682, 683, 687, 703

Offset: 1

dead

A023745 Plaindromes: numbers whose digits in base 3 are in nondecreasing order.

Original entry on oeis.org

0, 1, 2, 4, 5, 8, 13, 14, 17, 26, 40, 41, 44, 53, 80, 121, 122, 125, 134, 161, 242, 364, 365, 368, 377, 404, 485, 728, 1093, 1094, 1097, 1106, 1133, 1214, 1457, 2186, 3280, 3281, 3284, 3293, 3320, 3401, 3644, 4373, 6560, 9841, 9842, 9845, 9854

Offset: 1

Olivier Gérard

			In base 3 these numbers are 0, 1, 2, 11, 12, 22, 111, 112, 122, 222, 1111, 1112, ... [corrected by _Sean A. Irvine_, Jun 10 2019]

Harvey P. Dale, Table of n, a(n) for n = 1..1000
A. V. Kitaev, Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin, arXiv:1809.00122 [math.CA], 2018.

Cf. A023746 onwards. In base 2 we get A000225.

Select[Range[0,10000],!Negative[Min[Differences[IntegerDigits[ #,3]]]]&] (* or *) With[{nn=10},FromDigits[#,3]&/@Union[Flatten[Table[ PadRight[ PadLeft[{},n,1],x,2],{n,0,nn},{x,0,nn}],1]]] (* Harvey P. Dale, Oct 12 2011 *)
Select[Range[0,10000],LessEqual@@IntegerDigits[#,3]&] (* Ray Chandler, Jan 06 2014 *)

from math import isqrt
def A023745(n): return (3**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+3**(n-1-(a*(a+1)>>1))>>1)-1 # Chai Wah Wu, Apr 08 2025

Numbers that in ternary are the concatenation of i 1's with j 2's, i, j>=0. Also a(n) = A073216(n+1) - 1. Proof: Write a(n) as 1{m}2{n}, then adding 1 gives 1{m-1}20{n} for m>0 and 10{n} for m=0. Doubling yields 10{m-1}10{n} or 20{n}, respectively. These two forms exactly describe the forms of sums of two powers of 3, the two powers being 3^n and 3^(m+n). - Hugo van der Sanden

Change offset to 1 by Ray Chandler, Jan 06 2014

A329294 Numbers whose digits are in nondecreasing order in bases 4 and 5.

Original entry on oeis.org

0, 1, 2, 3, 6, 7, 31, 43, 63, 343

Offset: 1

Jon E. Schoenfield, Nov 09 2019

There are no more terms through 10^10000 (which is a 16610-digit number in base 4 and a 14307-digit number in base 5). But can it be proved that 343 is the final term of the sequence?

			a(1)  =   0 =     0_4 =    0_5
a(2)  =   1 =     1_4 =    1_5
a(3)  =   2 =     2_4 =    2_5
a(4)  =   3 =     3_4 =    3_5
a(5)  =   6 =    12_4 =   11_5
a(6)  =   7 =    13_4 =   12_5
a(7)  =  31 =   133_4 =  111_5
a(8)  =  43 =   223_4 =  133_5
a(9)  =  63 =   333_4 =  223_5
a(10) = 343 = 11113_4 = 2333_5

Intersection of A023746 (base 4) and A023747 (base 5).

Numbers whose digits are in nondecreasing order in bases b and b+1: this sequence (b=4), A329295 (b=5), A329296 (b=6), A329297 (b=7), A329298 (b=8), A329299 (b=9). See A329300 for the (apparently) largest term of each of these sequences.

isnondec(v) = (#v==0) || (#select(x->(x<0), vector(#v-1, k, v[k+1]-v[k])) == 0);
isok(n) = isnondec(digits(n, 4)) && isnondec(digits(n, 5)); \\ Michel Marcus, Nov 11 2019

A023752 Plaindromes: numbers whose digits in base 11 are in nondecreasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 37, 38, 39, 40, 41, 42, 43, 48, 49, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 72, 73, 74, 75, 76, 84, 85, 86, 87, 96, 97, 98, 108, 109, 120

Offset: 1

Olivier Gérard

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

Cf. A023746-A023757. - Omar E. Pol, Oct 20 2011

Select[Range[0,250],And@@NonNegative/@Differences[IntegerDigits[#,11]]&] (* Harvey P. Dale, Oct 20 2011 *)
Select[Range[0,120],LessEqual@@IntegerDigits[#,11]&] (* Ray Chandler, Jan 06 2014 *)

Change offset to 1 by Ray Chandler, Jan 06 2014

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A031989 Duplicate of A023746.

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A023745 Plaindromes: numbers whose digits in base 3 are in nondecreasing order.

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A329294 Numbers whose digits are in nondecreasing order in bases 4 and 5.

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A023752 Plaindromes: numbers whose digits in base 11 are in nondecreasing order.

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