A011533 -id:A011533 - cp's OEIS frontend

A293873 Numbers having '13' as substring of their digits.

13, 113, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 213, 313, 413, 513, 613, 713, 813, 913, 1013, 1113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 1213, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 1310, 1311, 1312, 1313, 1314, 1315

Offset: 1

M. F. Hasler, Oct 18 2017

Row 13 of A292690 and A293869. A121033 is the subsequence of multiples of 13.

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, A293874, A293875, A293876, A293877, A293878, A293879, A293880: same for '10' - '20'.
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[1350],SequenceCount[IntegerDigits[#],{1,3}]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 31 2017 *)

is_A293873 = has(n, p=13, m=10^#Str(p))=until(p>n\=10, n%m==p&&return(1))

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

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

Original entry on oeis.org

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

A212525 Primes containing a digit 3.

Original entry on oeis.org

3, 13, 23, 31, 37, 43, 53, 73, 83, 103, 113, 131, 137, 139, 163, 173, 193, 223, 233, 239, 263, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 431, 433, 439, 443, 463, 503, 523, 563, 593, 613, 631, 643, 653, 673, 683

Offset: 1

Jaroslav Krizek, Jun 12 2012

Supersequence of A045709, A106103 and A106099. Subsequence of A011533 and A062667.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A045709 (primes with first digit 3), A011533 (numbers containing a digit 3), A062667 (numbers n such that every divisor of n (except 1) contains the digit 3), A106099 (primes with maximal digit = 3), A106103 (primes with minimal digit = 3), A038611 (primes not containing digit 3).

Select[Prime[Range[200]], MemberQ[IntegerDigits[#], 3] &] (* T. D. Noe, Jun 12 2012 *)

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

A043503 Numbers having three 3's in base 10.

Original entry on oeis.org

333, 1333, 2333, 3033, 3133, 3233, 3303, 3313, 3323, 3330, 3331, 3332, 3334, 3335, 3336, 3337, 3338, 3339, 3343, 3353, 3363, 3373, 3383, 3393, 3433, 3533, 3633, 3733, 3833, 3933, 4333, 5333, 6333, 7333, 8333, 9333, 10333

Offset: 1

Clark Kimberling

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

Subsequence of A011533.

Select[Range[11000],DigitCount[#,10,3]==3&] (* Harvey P. Dale, Apr 13 2015 *)

A043502 Numbers having two 3's in base 10.

Original entry on oeis.org

33, 133, 233, 303, 313, 323, 330, 331, 332, 334, 335, 336, 337, 338, 339, 343, 353, 363, 373, 383, 393, 433, 533, 633, 733, 833, 933, 1033, 1133, 1233, 1303, 1313, 1323, 1330, 1331, 1332, 1334, 1335, 1336, 1337, 1338, 1339, 1343

Offset: 1

Clark Kimberling

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

Subsequence of A011533.

Select[Range[5000], DigitCount[#, 10, 3]==2&] (* Vincenzo Librandi, Jul 01 2015 *)

A043504 Numbers having four 3's in base 10.

Original entry on oeis.org

3333, 13333, 23333, 30333, 31333, 32333, 33033, 33133, 33233, 33303, 33313, 33323, 33330, 33331, 33332, 33334, 33335, 33336, 33337, 33338, 33339, 33343, 33353, 33363, 33373, 33383, 33393, 33433, 33533, 33633, 33733

Offset: 1

Clark Kimberling

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

Subsequence of A011533.

Select[Range[34000],DigitCount[#,10,3]==4&]  (* Harvey P. Dale, Feb 02 2011 *)

cp's OEIS Frontend

A293873 Numbers having '13' as substring of their digits.

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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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A212525 Primes containing a digit 3.

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A043503 Numbers having three 3's in base 10.

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A043502 Numbers having two 3's in base 10.

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A043504 Numbers having four 3's in base 10.

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