A011535 -id:A011535 - cp's OEIS frontend

A293880 Numbers having '20' as substring of their digits.

20, 120, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 220, 320, 420, 520, 620, 720, 820, 920, 1020, 1120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 1220, 1320, 1420, 1520, 1620, 1720, 1820, 1920, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010

Offset: 1

M. F. Hasler, Oct 18 2017

Row 20 of A292690 and A293869. A121040 lists the terms which are divisible by 19.

Index entries for 10-automatic sequences

Cf. A292690, A293869.
Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539: analog for '0' - '9'.
Cf. A293870, A293871, A293872, A293873, A293874, A293875, A293876, A293877, A293878, A293879: same for '10' - '19'.
Cf. A121041, A121022, A121023, A121024, A121025, A121026, A121027, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040: subsequences of the above, containing only multiples of the pattern p.

Select[Range[2100],SequenceCount[IntegerDigits[#],{2,0}]>0&] (* Harvey P. Dale, Jul 25 2021 *)

is_A293880 = has(n, p=20, m=10^#Str(p))=until(p>n\=10, n%m==p&&return(1))

a(n) ~ n. - Charles R Greathouse IV, Nov 02 2022

A175688 Numbers k with property that arithmetic mean of its digits is both an integer and one of the digits of k.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 102, 111, 120, 123, 132, 135, 147, 153, 159, 174, 195, 201, 204, 210, 213, 222, 231, 234, 240, 243, 246, 258, 264, 285, 306, 312, 315, 321, 324, 333, 342, 345, 351, 354, 357, 360, 369, 375, 396, 402

Offset: 1

Claudio Meller, Aug 09 2010

Subsequence of A061383.

A180160(a(n)) = 0. - Reinhard Zumkeller, Aug 15 2010

			135 is in the list because (1+3+5)/3 = 3 and 3 is a digit of 135.

R. Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A007953, A055642, A004426, A004427; A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539.

Cf. A052018. - Reinhard Zumkeller, Aug 15 2010

a175688 n = a175688_list !! (n-1)
a175688_list = filter f [0..] where
   f x = m == 0 && ("0123456789" !! avg) `elem` show x
         where (avg, m) = divMod (a007953 x) (a055642 x)
-- Reinhard Zumkeller, Jun 18 2013

idQ[n_]:=Module[{idn=IntegerDigits[n],m},m=Mean[idn];IntegerQ[m] && MemberQ[idn,m]]; Select[Range[0,500],idQ] (* Harvey P. Dale, Jun 10 2011 *)

Edited by Reinhard Zumkeller, Aug 13 2010

A257667 Primes containing a digit 5.

Original entry on oeis.org

5, 53, 59, 151, 157, 251, 257, 353, 359, 457, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 653, 659, 751, 757, 853, 857, 859, 953, 1051, 1151, 1153, 1259, 1451, 1453, 1459, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579

Offset: 1

Vincenzo Librandi, May 03 2015

Subsequence of primes of A011535. - Michel Marcus, May 03 2015

Primes in A062671. - Bruno Berselli, May 03 2015

Shujing Lyu, Table of n, a(n) for n = 1..100000

Cf. prime numbers containing the string k: A208270 (k=1), A208272 (k=2), A212525 (k=3), this sequence (k=5), A257668 (k=7), A166571 (k=10), A166572 (k=11), A243529 (k=12), A166573 (k=13), A243530 (k=14), A243531 (k=15), A243532 (k=16), A166579 (k=17), A243527 (k=111), A166580 (k=222), A166581 (k=333), A166582 (k=444).

Cf. A011535, A062671, A243531 (subsequence).

[p: p in PrimesUpTo(1600) | 5 in Intseq(p)];

Select[Prime[Range[250]], ! StringFreeQ[ToString[#], "5"] &]

forprime(p=1, 1600, if(vecsearch(vecsort(digits(p)), 5), print1(p, ", "))) \\ Derek Orr, May 05 2015; corrected by Michel Marcus, Oct 30 2023

[p for p in primes(1600) if 5 in p.digits(base=10)] # Bruno Berselli, May 03 2015

a(n) ~ n log n. - Charles R Greathouse IV, Nov 01 2022

A283608 Numbers whose largest decimal digit is 5.

Original entry on oeis.org

5, 15, 25, 35, 45, 50, 51, 52, 53, 54, 55, 105, 115, 125, 135, 145, 150, 151, 152, 153, 154, 155, 205, 215, 225, 235, 245, 250, 251, 252, 253, 254, 255, 305, 315, 325, 335, 345, 350, 351, 352, 353, 354, 355, 405, 415, 425, 435, 445, 450, 451, 452, 453, 454

Offset: 1

Jaroslav Krizek, Mar 19 2017

Numbers n such that A054055(n) = 5.
Number of terms less than 10^n is 6^n - 5^n.
Subsequence of A011535. - David A. Corneth, Mar 25 2017
Prime terms are in A106097.

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Cf. A011535, A054055, A106097.

Cf. Sequences of numbers whose largest decimal digit is k (for k = 1..9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), this sequence (k = 5), A283609 (k = 6), A283610 (k = 7), A283611 (k = 8), A011539 (k = 9).

Filtered([1..500],n->Maximum(ListOfDigits(n))=5); # Muniru A Asiru, Feb 27 2019

[n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 5];

Select[Range[1000], Max[IntegerDigits[#]] == 5 &] (* Giovanni Resta, Mar 19 2017 *)

for(n=1, 500, if(vecmax(digits(n))==5, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

nxt(n) = {my(d = digits(n), i, j=0, t=0); forstep(i=#d,1,-1, if(d[i]!=5, j=i; break)); if(j>0, d[j]++; if(d[j]==5, for(k=j+1,#d,d[k]=0)); if(j<#d && d[j+1]==5, for(k=j+1,#d-1,d[k]=0)); for(k=1,j-1, if(d[k]==5,for(i=j+1, #d, d[i] = 0);break)), d = vector(#d+1); d[1]=1; d[#d]=5);sum(i=1, #d, d[i]*10^(#d-i))} \\ David A. Corneth, Mar 25 2017

from sympy.ntheory.factor_ import digits
print([n for n in range(1, 501) if max(digits(n)[1:])==5]) # Indranil Ghosh, Mar 19 2017

A043510 Numbers having two 5's in base 10.

Original entry on oeis.org

55, 155, 255, 355, 455, 505, 515, 525, 535, 545, 550, 551, 552, 553, 554, 556, 557, 558, 559, 565, 575, 585, 595, 655, 755, 855, 955, 1055, 1155, 1255, 1355, 1455, 1505, 1515, 1525, 1535, 1545, 1550, 1551, 1552, 1553, 1554, 1556

Offset: 1

Clark Kimberling

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Subsequence of A011535.

Select[Range[1600],DigitCount[#,10,5]==2&] (* Harvey P. Dale, Sep 01 2021 *)

A043511 Numbers having three 5's in base 10.

Original entry on oeis.org

555, 1555, 2555, 3555, 4555, 5055, 5155, 5255, 5355, 5455, 5505, 5515, 5525, 5535, 5545, 5550, 5551, 5552, 5553, 5554, 5556, 5557, 5558, 5559, 5565, 5575, 5585, 5595, 5655, 5755, 5855, 5955, 6555, 7555, 8555, 9555, 10555

Offset: 1

Clark Kimberling

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Subsequence of A011535.

Select[Range[555,11000],DigitCount[#,10,5]==3&] (* Harvey P. Dale, May 31 2021 *)

A043512 Numbers having four 5's in base 10.

Original entry on oeis.org

5555, 15555, 25555, 35555, 45555, 50555, 51555, 52555, 53555, 54555, 55055, 55155, 55255, 55355, 55455, 55505, 55515, 55525, 55535, 55545, 55550, 55551, 55552, 55553, 55554, 55556, 55557, 55558, 55559, 55565, 55575

Offset: 1

Clark Kimberling

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Subsequence of A011535.

A124694 Sets of digits such that the product of the digits is 10 times the sum of the digits. Each set is arranged as a number with nondecreasing digits.

Original entry on oeis.org

459, 1566, 2259, 2355, 11558, 12445, 111567, 112356, 122245, 1113345, 1222225, 11111568, 11112357, 11112455, 11122335, 111122255, 1111111569, 1111112358, 11111111578, 11111112456, 111111112359, 111111112555, 111111113445

Offset: 1

Tanya Khovanova, Dec 25 2006

4*5*9 = 180 and 4 + 5 + 9 = 18.

Each term must include the digit 5, so it is a subsequence of A011535. - Chai Wah Wu, Dec 08 2015

Chai Wah Wu, Table of n, a(n) for n = 1..931

A062043 (Numbers for which the product of the digits is 10 times their sum) is created by permuting digits in every number of this sequence.

FromDigits /@ DeleteDuplicates@ Map[Sort, IntegerDigits@ Select[Range[10^7], Times @@ # == 10 Total@ # &@ IntegerDigits@ # &]] (* Michael De Vlieger, Dec 09 2015 *)

Extended by D. S. McNeil, Dec 16 2010

cp's OEIS Frontend

A293880 Numbers having '20' as substring of their digits.

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A175688 Numbers k with property that arithmetic mean of its digits is both an integer and one of the digits of k.

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A257667 Primes containing a digit 5.

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A283608 Numbers whose largest decimal digit is 5.

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A043510 Numbers having two 5's in base 10.

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A043511 Numbers having three 5's in base 10.

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A043512 Numbers having four 5's in base 10.

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A124694 Sets of digits such that the product of the digits is 10 times the sum of the digits. Each set is arranged as a number with nondecreasing digits.

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