A032810 -id:A032810 - cp's OEIS frontend

A284922 Numbers with digits 2 and 8 only.

2, 8, 22, 28, 82, 88, 222, 228, 282, 288, 822, 828, 882, 888, 2222, 2228, 2282, 2288, 2822, 2828, 2882, 2888, 8222, 8228, 8282, 8288, 8822, 8828, 8882, 8888, 22222, 22228, 22282, 22288, 22822, 22828, 22882, 22888, 28222, 28228, 28282, 28288, 28822, 28828

Offset: 1

Jaroslav Krizek, Apr 05 2017

All terms are even.

Cf. Numbers with digits 2 and k only for k = 0 - 1 and 3 - 9: A169965 (k = 0), A007931 (k = 1), A032810 (k = 3), A284920 (k = 4), A072961 (k = 5), A284632 (k = 6), A284921 (k = 7), this sequence (k = 8), A284923 (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {2, 8}]

Flatten@ Array[FromDigits /@ Tuples[{2, 8}, #] &, 5] (* Michael De Vlieger, Apr 06 2017 *)

a(n) = 2 * A032822(n).

A284923 Numbers with digits 2 and 9 only.

Original entry on oeis.org

2, 9, 22, 29, 92, 99, 222, 229, 292, 299, 922, 929, 992, 999, 2222, 2229, 2292, 2299, 2922, 2929, 2992, 2999, 9222, 9229, 9292, 9299, 9922, 9929, 9992, 9999, 22222, 22229, 22292, 22299, 22922, 22929, 22992, 22999, 29222, 29229, 29292, 29299, 29922, 29929

Offset: 1

Jaroslav Krizek, Apr 06 2017

Prime terms are in A020460.

Numbers with digits 2 and k only for k = 0 - 1 and 3 - 9: A169965 (k = 0), A007931 (k = 1), A032810 (k = 3), A284920 (k = 4), A072961 (k = 5), A284632 (k = 6), A284921 (k = 7), A284922 (k = 8), this sequence (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {2, 9}]

Select[Range[30000],SubsetQ[{2,9},Sort[DeleteDuplicates[IntegerDigits[#]]]] &] (* Stefano Spezia, Aug 06 2025 *)

A213971 List of primitive words over the alphabet {2,3}.

Original entry on oeis.org

2, 3, 23, 32, 223, 232, 233, 322, 323, 332, 2223, 2232, 2233, 2322, 2332, 2333, 3222, 3223, 3233, 3322, 3323, 3332, 22223, 22232, 22233, 22322, 22323, 22332, 22333, 23222, 23223, 23232, 23233, 23322, 23323, 23332, 23333, 32222, 32223, 32232, 32233, 32322, 32323, 32332, 32333, 33222, 33223, 33232, 33233, 33322, 33323, 33332

Offset: 1

N. J. A. Sloane, Jun 30 2012

A word w is primitive if it cannot be written as u^k with k>1; otherwise it is imprimitive.
The {0,1} version of this sequence is
0, 1, 01, 10, 001, 010, 011, 100, 101, 110, 0001, 0010, 0011, 0100, 0110, 0111, 1000, 1001, 1011, 1100, 1101, 1110, 00001, 00010, 00011, 00100, 00101, 00110, 00111, 01000, 01001, 01010, 01011, 01100, 01101, 01110, 01111, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, ...,
but this cannot be included as a sequence in the OEIS since it contains nonzero "numbers" beginning with 0.
The Lyndon words over {2,3} are the intersection of this sequence with A239016. - M. F. Hasler, Mar 10 2014
This sequence results from A213970 by replacing all digits 1 by 2, and from A213969 by replacing all digits 2 by 3 and digits 1 by 2. - M. F. Hasler, Mar 10 2014

A. de Luca and S. Varricchio, Finiteness and Regularity in Semigroups and Formal Languages, Monographs in Theoretical Computer Science, Springer-Verlag, Berlin, 1999. See p. 10.

Cf. A213969-A213974.

for(n=1, 5, p=vector(n, i, 10^(n-i))~; forvec(d=vector(n, i, [2, 3]), is_A239017(m=d*p)&&print1(m", "))) \\ M. F. Hasler, Mar 10 2014

A213971 = A032810 intersect A239017. - M. F. Hasler, Mar 10 2014

A176892 Decimal representation of the reverted binary representation of n followed by digits substitution 0->2, 1->3.

Original entry on oeis.org

2, 3, 23, 33, 223, 323, 233, 333, 2223, 3223, 2323, 3323, 2233, 3233, 2333, 3333, 22223, 32223, 23223, 33223, 22323, 32323, 23323, 33323, 22233, 32233, 23233, 33233, 22333, 32333, 23333, 33333, 222223, 322223, 232223, 332223, 223223

Offset: 0

Roger L. Bagula, Apr 28 2010

Revert the digits of A007088(n), preserving zeros, and increase each digit by 2 (add the repunit A002276 with the same number of digits).

			n=10 is A007088(10)= 1010 in binary, reverted 0101. Adding 2222 generates a(10)=2323.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A007088, A002276, A032810.

import Data.List (unfoldr); import Data.Tuple (swap)
a176892 0 = 2a176892 n = foldl (\v d -> 10 * v + d + 2) 0 $
   unfoldr (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2) n
-- Reinhard Zumkeller, Jul 16 2015

Table[Sum[Table[((IntegerDigits[ n, 2]) /. 0 -> 2) /. 1 -> 3, {n, 0, 50}][[n]][[m]]*10^(m - 1),
{m, 1, Length[Table[((IntegerDigits[n, 2]) /. 0 -> 2) /. 1 -> 3, {n, 0, 50}][[n]]]}], {n, 1, 51}]

A284963 Numbers with digits 3 and 8 only.

Original entry on oeis.org

3, 8, 33, 38, 83, 88, 333, 338, 383, 388, 833, 838, 883, 888, 3333, 3338, 3383, 3388, 3833, 3838, 3883, 3888, 8333, 8338, 8383, 8388, 8833, 8838, 8883, 8888, 33333, 33338, 33383, 33388, 33833, 33838, 33883, 33888, 38333, 38338, 38383, 38388, 38833, 38838

Offset: 1

Jaroslav Krizek, Apr 06 2017

Prime terms are in A020464.

Numbers with digits 3 and k only for k = 0 - 2 and 4 - 9: A169966 (k = 0), A032917 (k = 1), A032810 (k = 2), A032834 (k = 4), A284379 (k = 5), A284633 (k = 6), A143967 (k = 7), this sequence (k = 8), A284964 (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {3, 8}]

Table[FromDigits/@Tuples[{3,8},n],{n,5}]//Flatten (* Harvey P. Dale, Mar 23 2021 *)

A284964 Numbers with digits 3 and 9 only.

Original entry on oeis.org

3, 9, 33, 39, 93, 99, 333, 339, 393, 399, 933, 939, 993, 999, 3333, 3339, 3393, 3399, 3933, 3939, 3993, 3999, 9333, 9339, 9393, 9399, 9933, 9939, 9993, 9999, 33333, 33339, 33393, 33399, 33933, 33939, 33993, 33999, 39333, 39339, 39393, 39399, 39933, 39939

Offset: 1

Jaroslav Krizek, Apr 06 2017

All terms > 3 are composite.

Cf. Numbers with digits 3 and k only for k = 0 - 2 and 4 - 9: A169966 (k = 0), A032917 (k = 1), A032810 (k = 2), A032834 (k = 4), A284379 (k = 5), A284633 (k = 6), A143967 (k = 7), A284963 (k = 8), this sequence (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {3, 9}]

Table[FromDigits/@Tuples[{3,9},n],{n,5}]//Flatten (* Harvey P. Dale, Sep 20 2022 *)

a(n) = 3 * A032917(n).

A166713 Alliterative-digit numbers: Positive integers n such that the English names of the decimal digits of n begin with the same letter; ignore single-digit numbers.

Original entry on oeis.org

11, 22, 23, 32, 33, 44, 45, 54, 55, 66, 67, 76, 77, 88, 99, 111, 222, 223, 232, 233, 322, 323, 332, 333, 444, 445, 454, 455, 544, 545, 554, 555, 666, 667, 676, 677, 766, 767, 776, 777, 888, 999, 1111, 2222, 2223, 2232, 2233, 2322, 2323, 2332, 2333, 3222, 3223

Offset: 1

Rick L. Shepherd, Oct 19 2009

The multi-digit repdigits (A014181) are a subsequence. No term contains the digit 0 (zero). All terms containing digits 1 (one), 8 (eight), or 9 (nine) are also terms of A014181. Any term not mentioned above is a string of 2's (twos) and 3's (threes) only (a multi-digit term of A032810), 4's (fours) and 5's (fives) only, or 6's (sixes) and 7's (sevens) only.

			454 is a term as digits "four", "five", "four" each begin with the letter "f".

Cf. A146755, A014181, A032810.

cp's OEIS Frontend

A284922 Numbers with digits 2 and 8 only.

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A284923 Numbers with digits 2 and 9 only.

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A213971 List of primitive words over the alphabet {2,3}.

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A176892 Decimal representation of the reverted binary representation of n followed by digits substitution 0->2, 1->3.

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A284963 Numbers with digits 3 and 8 only.

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A284964 Numbers with digits 3 and 9 only.

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A166713 Alliterative-digit numbers: Positive integers n such that the English names of the decimal digits of n begin with the same letter; ignore single-digit numbers.

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