A014181 -id:A014181 - cp's OEIS frontend

A033023 Numbers whose base-10 expansion has no run of digits with length < 2.

11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1100, 1111, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 2200, 2211, 2222, 2233, 2244, 2255, 2266, 2277, 2288, 2299, 3300, 3311, 3322, 3333

Offset: 1

Clark Kimberling

Contains A014181 as subsequence. A115853 is a supersequence. - M. F. Hasler, Jun 24 2016

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1100 terms from Vincenzo Librandi)
Giovanni Resta, Zygodrome

Cf. A014181, A115853.

Select[Range[10000], Min[Length/@Split[IntegerDigits[#, 10]]]>1&] (* Vincenzo Librandi, Feb 05 2014 *)

is(n)={n=digits(n);while(#n>2 && n[2]==n[1], n=if(n[3]==n[1],n[^1],n[3..-1]));#n>1&&n[1]==n[2]} \\ M. F. Hasler, Jun 24 2016

A115853 Numbers where every digit that is present occurs more than once (not necessarily consecutively).

Original entry on oeis.org

11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1001, 1010, 1100, 1111, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 1212, 1221, 1313, 1331, 1414, 1441, 1515, 1551, 1616, 1661, 1717, 1771, 1818, 1881, 1919, 1991, 2002

Offset: 1

Franklin T. Adams-Watters, Mar 13 2006

Through terms shown, this is also numbers where every digit present occurs the same number of times (not necessarily consecutively). The first number in this sequence not in that one is 10001.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A033023, A014181.

filter:= proc(n)
local L,S;
L:= convert(n,base,10);
S:= convert(L,set);
min(seq(numboccur(i,L),i=S)) > 1
end proc:
select(filter, [$1..10000]); # Robert Israel, May 28 2014

edQ[n_]:=Min[Select[DigitCount[n],#!=0&]]>1; Select[Range[2100],edQ] (* Harvey P. Dale, Dec 13 2018 *)

A179309 The smallest number that has more copies of some digit than any previous number in the sequence.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1000, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 10000, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 100000

Offset: 1

Jack W Grahl, Jul 10 2010

These are, for each digit d and each natural number k, the smallest positive number in which the digit d appears k (or more) times, in numerical order. They are all numbers with all digits repeated except numbers of the form 10^m.

If we started with 0 the term 10 would be missed and all other terms would be the same.

			100 is included because no previous term contains two 0's. 111 is included because no previous term contains more than 2 1's. Every number between 101 and 110 inclusive is omitted because each contains at most 2 1's (no more than 11) and at most 1 of any other digit (no more than 2 thru 10).

Supersequence of A014181 and A010785. See also A179310.

With[{nn=5},Join[Flatten[Table[FromDigits[PadRight[{},i,n]],{i,nn},{n,9}]],10^Range[nn]]]//Sort (* Harvey P. Dale, May 31 2016 *)

A288068 Repdigits in base 10 which are Brazilian numbers.

Original entry on oeis.org

7, 8, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111, 222222, 333333, 444444, 555555, 666666, 777777, 888888, 999999

Offset: 1

Bernard Schott, Jun 05 2017

These numbers are all repdigits belonging to A010785. The representation of the numbers 7 and 8 in base 10 is not Brazilian but they are yet Brazilian because 7 = 111_2 and 8 = 22_3. Except the repdigits 7, 8, 22, 33, 55, 77 and the primes repunits R_n from A004022 and A004023, all these Brazilian repdigits are also Brazilian in another base.

Contains all base-10 repdigits (A010785) >= 22, because these are Brazilian numbers in base 10. - R. J. Mathar, Jul 19 2024

			7 = 111_2;
44 = 44_10 = 22_21;
66 = 66_10 = 33_21 = 22_32.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, -10).

Cf. A004022, A004023, A010785, A014181, A125134,

# reuses code of A125134, b-file output
n := 1 :
for ndigs from 1 do
    for d from 1 to 9 do
        r := add(d*10^i,i=0..ndigs-1) ; # rep digit d in base 10
        if isA125134(r) then
            printf("%d %d\n",n,r) ;
            n := n+1 ;
        end if;
    end do:
end do: # R. J. Mathar, Jul 19 2024

Select[Flatten@ Table[FromDigits@ ConstantArray[k, n], {n, 6}, {k, 9}], Function[n, Length@ SelectFirst[Range[2, n - 2], Count[DigitCount[n, #], ?(# > 0 &)] == 1 &] == 0]] (* _Michael De Vlieger, Jun 06 2017, Version 10 *)

A347189 Positive integers that can be expressed as the sum of powers of their digits (from right to left) with consecutive natural exponents.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 24, 332, 1676, 121374, 4975929, 134116265, 1086588775, 3492159897, 8652650287, 8652650482

Offset: 1

Reiner Moewald, Aug 21 2021

Any number > 9 consisting of just one digit (A014181) can't be in the list. (Provable using the Carmichael function.)

			24 = 4^2 + 2^3 is a term.
332 = 2^3 + 3^4 + 3^5 is another term.

Cf. A023052, A032799, A014181.

liste = []
for ex in range(0, 20):
    for t in range(1, 10000):
        n = t
        pot = ex
        ergebnis = 0
        while n > 0:
            pot = pot + 1
            rest = n % 10
            n = (n - rest) // 10
            zw = 1
            for i in range(pot):
                zw = zw * rest
            ergebnis = ergebnis + zw
        if (int(ergebnis) == t) and (t not in liste):
            liste.append(t)
liste.sort()
print(liste)

def powsum(digits, startexp):
    return sum(digits[i]**(startexp+i) for i in range(len(digits)))
def ok(n):
    if n < 10: return True
    s = str(n)
    if set(s) <= {'0', '1'}: return False
    digits, startexp = list(map(int, s))[::-1], 1
    while powsum(digits, startexp) < n: startexp += 1
    return n == powsum(digits, startexp)
print(list(filter(ok, range(2*10**5)))) # Michael S. Branicky, Aug 29 2021

a(15)-a(19) from Michael S. Branicky, Aug 31 2021

A084434 Numbers whose digit permutations have GCD > 1.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 18, 20, 21, 22, 24, 26, 27, 28, 30, 33, 36, 39, 40, 42, 44, 45, 46, 48, 50, 51, 54, 55, 57, 60, 62, 63, 64, 66, 68, 69, 70, 72, 75, 77, 78, 80, 81, 82, 84, 86, 87, 88, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132

Offset: 1

Amarnath Murthy, Jun 02 2003

Numbers k such that there is a number d>1 which divides every number that can be obtained by permuting the digits of k. - N. J. A. Sloane, Aug 27 2020

Theorem. The sequence consists of: (1) A008585 (multiples of 3), (2) A014263 (numbers with all digits even), (3) A014181 (numbers with all digits equal), (4) numbers with all digits 5 or 0, (5) numbers with all digits 7 or 0, (6) numbers with 6k digits, all of which are 1 or 8, and (7) numbers with 6k digits, all of which are 2 or 9. - David Wasserman, May 07 2004

			72 is in the sequence because 72 and 27 are both divisible by 9.

Cf. A008585, A014181, A014263, A071249.

Subsequence of A084433 which contains for example 592 which is not in here.

Select[Range[0, 150], GCD @@ FromDigits /@ Permutations[IntegerDigits[#]] > 1 &]  (* Harvey P. Dale, Jan 12 2011 *)

More terms from David Wasserman, May 07 2004
Initial zero removed, Harvey P. Dale, Jan 14 2011
Entry revised by N. J. A. Sloane, Aug 27 2020

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

A033023 Numbers whose base-10 expansion has no run of digits with length < 2.

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A115853 Numbers where every digit that is present occurs more than once (not necessarily consecutively).

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A179309 The smallest number that has more copies of some digit than any previous number in the sequence.

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Mathematica

A288068 Repdigits in base 10 which are Brazilian numbers.

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Maple

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A347189 Positive integers that can be expressed as the sum of powers of their digits (from right to left) with consecutive natural exponents.

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A084434 Numbers whose digit permutations have GCD > 1.

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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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