A011538 -id:A011538 - 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

A257225 Numbers that have at least one divisor containing the digit 8 in base 10.

Original entry on oeis.org

8, 16, 18, 24, 28, 32, 36, 38, 40, 48, 54, 56, 58, 64, 68, 72, 76, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 96, 98, 104, 108, 112, 114, 116, 118, 120, 126, 128, 136, 138, 140, 144, 148, 152, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178

Offset: 1

Jaroslav Krizek, May 07 2015

Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 8.

A011538 (numbers that contain an 8) is a subsequence. - Michel Marcus, May 19 2015

			18 is in sequence because the list of divisors of 18: (1, 2, 3, 6, 9, 18) contains digit 8.

Cf. A037278, A176558, A243360, A256824.

Cf. similar sequences with another digit: A209932 (0), A000027 (1), A257219 (2), A257220 (3), A257221 (4), A257222 (5), A257223 (6), A257224 (7), A257226 (9).

[n: n in [1..1000] | [8] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))];

select(t -> has(map(convert,numtheory:-divisors(t),base,10),8), [$1..200]); # Robert Israel, May 14 2015

Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 8] > 0 &]
Select[Range[200],SequenceCount[Flatten[IntegerDigits/@Divisors[#]],{8}]> 0&] (* Harvey P. Dale, Aug 02 2021 *)

is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 8), return(1))); 0

from itertools import count, islice
from sympy import divisors
def A257225_gen(): return filter(lambda n:any('8' in str(d) for d in divisors(n, generator=True)), count(1))
A257225_list = list(islice(A257225_gen(), 58)) # Chai Wah Wu, Dec 27 2021

a(n) ~ n.

Mathematica and PARI programs with assistance from Michael De Vlieger and Charles R Greathouse IV, respectively.

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

A284292 Primes containing a digit 8.

Original entry on oeis.org

83, 89, 181, 281, 283, 383, 389, 487, 587, 683, 787, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 983, 1087, 1181, 1187, 1283, 1289, 1381, 1481, 1483, 1487, 1489, 1583, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867

Offset: 1

Jaroslav Krizek, Mar 25 2017

Subsequence of A011538 and A062677.

Differs from A062677 which contains also the composites 6889 = 83^2, 7387 = 83*89, 23489=83*283, 25187=89*283, 31789 = 83*383 etc. - R. J. Mathar, Mar 27 2017

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

Cf. Primes containing a digit k for k = 0 - 9: A056709 (k = 0), A208270 (k = 1), A208272 (k = 2), A212525 (k = 3), A284290 (k = 4), A257667 (k = 5), A284291 (k = 6), A257668 (k = 7), this sequence (k = 8), A106093 (k = 9).

[p: p in PrimesUpTo(10000) | 8 in Intseq(p)];

isA284292 := proc(n)
    if isprime(n) then
        convert(convert(n,base,10),set) ;
        if 8 in % then
            true;
        else
            false;
        end if;
    else
        false;
    end if;
end proc:
for n from 1 to 2000 do
    if isA284292(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Mar 27 2017

Select[Prime@ Range@ 500, MemberQ[ IntegerDigits@ #, 8] &] (* Giovanni Resta, Mar 25 2017 *)

from sympy import primerange
print([n for n in primerange(2, 2000) if '8' in str(n)]) # Indranil Ghosh, Mar 25 2017

A043522 Numbers having two 8's in base 10.

Original entry on oeis.org

88, 188, 288, 388, 488, 588, 688, 788, 808, 818, 828, 838, 848, 858, 868, 878, 880, 881, 882, 883, 884, 885, 886, 887, 889, 898, 988, 1088, 1188, 1288, 1388, 1488, 1588, 1688, 1788, 1808, 1818, 1828, 1838, 1848, 1858, 1868, 1878

Offset: 1

Clark Kimberling

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

Subsequence of A011538.

Select[Range[2000],DigitCount[#,10,8]==2&]  (* Harvey P. Dale, Mar 20 2011 *)

A043523 Numbers having three 8's in base 10.

Original entry on oeis.org

888, 1888, 2888, 3888, 4888, 5888, 6888, 7888, 8088, 8188, 8288, 8388, 8488, 8588, 8688, 8788, 8808, 8818, 8828, 8838, 8848, 8858, 8868, 8878, 8880, 8881, 8882, 8883, 8884, 8885, 8886, 8887, 8889, 8898, 8988, 9888, 10888

Offset: 1

Clark Kimberling

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

Subsequence of A011538.

Select[Range[11000],DigitCount[#,10,8]==3&] (* Harvey P. Dale, May 25 2023 *)

A043524 Numbers having four 8's in base 10.

Original entry on oeis.org

8888, 18888, 28888, 38888, 48888, 58888, 68888, 78888, 80888, 81888, 82888, 83888, 84888, 85888, 86888, 87888, 88088, 88188, 88288, 88388, 88488, 88588, 88688, 88788, 88808, 88818, 88828, 88838, 88848, 88858, 88868

Offset: 1

Clark Kimberling

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

Subsequence of A011538.

Select[Range[100000],DigitCount[#,10,8]==4&] (* Harvey P. Dale, Oct 17 2019 *)

A134777 First digit of n alphabetically.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 4, 5, 1, 1, 8, 9, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 1, 3, 3, 4, 5, 6, 7, 8, 9, 4, 4, 4, 4, 4, 5, 4, 4, 8, 4, 5, 5, 5, 5, 5, 5, 5, 5, 8, 5, 6, 1, 6, 6, 4, 5, 6, 7, 8, 9, 7, 1, 7, 7, 4, 5, 7, 7, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 4, 5, 9, 9, 8, 9, 1, 1, 1, 1, 4

Offset: 0

Rick L. Shepherd, Nov 11 2007

Digits are decimal with names in English (see A000052). A134777(n)=A134778(n) iff n is a repdigit (n=A010785(m)), in which case a(n)=A010888(m), the repeated digit. a(n)=0 only for n=0. a(n)=8 iff n is a member of A011538.

			a(104) = 4 because the digits of 104 are 1 (one), 0 (zero) and 4 (four) and "four" occurs before both "one" and "zero" alphabetically.

Michael S. Branicky, Table of n, a(n) for n = 0..10000

Cf. A134778, A000052, A010785, A010888, A011538.

def alpha(n): return [8, 5, 4, 9, 1, 7, 6, 3, 2, 0].index(n)
def a(n): return sorted(map(int, str(n)), key=alpha)[0]
print([a(n) for n in range(105)]) # Michael S. Branicky, Dec 12 2023

A245877 Primes p such that p - d and p + d are also primes, where d is the largest digit of p.

Original entry on oeis.org

263, 563, 613, 653, 1613, 1663, 3463, 4643, 5563, 5653, 6263, 6323, 12653, 13463, 14633, 16063, 16223, 21163, 21563, 25463, 26113, 30643, 32063, 33623, 36313, 41263, 41603, 44263, 53623, 54623, 56003, 60133, 61553, 62213, 62633, 64013, 65413, 105613, 106213

Offset: 1

Colin Barker, Aug 05 2014

Intersection of A245742 and A245743.
The largest digit of a(n) is 6, and the least significant digit of a(n) is 3.
Intersection of A006489, A011536, and complements of A011537, A011538, A011539. - Robert Israel, Aug 05 2014

			The prime 263 is in the sequence because 263 - 6 = 257 and 263 + 6 = 269 are both primes.

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

Cf. A006489, A245742, A245743, A245744, A245745, A245878.

pdpQ[n_]:=Module[{m=Max[IntegerDigits[n]]},AllTrue[n+{m,-m},PrimeQ]]; Select[ Prime[Range[11000]],pdpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 13 2017 *)

select(p->d=vecsort(digits(p),,4)[1]; isprime(p-d) && isprime(p+d), primes(20000))

import sympy
from sympy import prime
from sympy import isprime
for n in range(1,10**5):
  s=prime(n)
  lst = []
  for i in str(s):
    lst.append(int(i))
  if isprime(s+max(lst)) and isprime(s-max(lst)):
    print(s,end=', ')
# Derek Orr, Aug 13 2014

A095790 Numbers whose name in English contains an "r".

Original entry on oeis.org

3, 4, 13, 14, 23, 24, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 53, 54, 63, 64, 73, 74, 83, 84, 93, 94, 103, 104, 113, 114, 123, 124, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148

Offset: 1

Michael Joseph Halm, Jul 10 2004

A008520 are numbers which contain an "e", A008540 an "f", A011538 a "g", A008536 an "n", A008519 an "o", A008538 an "s", A008522 a "t", A011534 a "u", A011532 a "w", A011536 an "x" and A008553 a "y"

			a(1) = 3 because "three" contains an "r", 0, 1 and 2 do not

Cf. A008520, A008540, A011538, A008536, A008519, A008538, A008522, A011534, A011532, A011536, A008553.

cp's OEIS Frontend

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

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A257225 Numbers that have at least one divisor containing the digit 8 in base 10.

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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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A284292 Primes containing a digit 8.

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A043522 Numbers having two 8's in base 10.

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A043523 Numbers having three 8's in base 10.

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A043524 Numbers having four 8's in base 10.

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A134777 First digit of n alphabetically.

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