A011537 -id:A011537 - 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

A257224 Numbers that have at least one divisor containing the digit 7 in base 10.

Original entry on oeis.org

7, 14, 17, 21, 27, 28, 34, 35, 37, 42, 47, 49, 51, 54, 56, 57, 63, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 84, 85, 87, 91, 94, 97, 98, 102, 105, 107, 108, 111, 112, 114, 117, 119, 126, 127, 133, 134, 135, 136, 137, 140, 141, 142, 144, 146, 147, 148

Offset: 1

Jaroslav Krizek, May 05 2015

Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 7.

A011537 (numbers that contain a 7) is a subsequence. - Michel Marcus, May 25 2015

			14 is in sequence because the list of divisors of 14: (1, 2, 7, 14) contains digit 7.

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), A257225 (8), A257226 (9).

[n: n in [1..1000] | [7] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))];

Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 7] > 0 &]

is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 7), return(1))); 0

from itertools import count, islice
from sympy import divisors
def A257224_gen(): return filter(lambda n:any('7' in str(d) for d in divisors(n, generator=True)), count(1))
A257224_list = list(islice(A257224_gen(), 60)) # 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

A257668 Primes containing a digit 7.

Original entry on oeis.org

7, 17, 37, 47, 67, 71, 73, 79, 97, 107, 127, 137, 157, 167, 173, 179, 197, 227, 257, 271, 277, 307, 317, 337, 347, 367, 373, 379, 397, 457, 467, 479, 487, 547, 557, 571, 577, 587, 607, 617, 647, 673, 677, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761

Offset: 1

Vincenzo Librandi, May 03 2015

Primes in A062675.

Subsequence of primes of A011537. - Michel Marcus, May 03 2015

			For n = 2, a(2) = 17 is the second prime containing a digit of 7.

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

Cf. similar sequences listed in A257667.

Cf. A011537, A062675, A166579 (subsequence).

[p: p in PrimesUpTo(800) | 7 in Intseq(p)];

Select[Prime[Range[150]], ! StringFreeQ[ToString[#], "7"] &]

lista(nn) = forprime(p=2, nn, if(vecsearch(vecsort(digits(p)), 7), print1(p, ", "))); \\ Altug Alkan, Apr 21 2016; corrected by Michel Marcus, Oct 30 2023

[p for p in primes(800) if 7 in p.digits(base=10)] # Bruno Berselli, May 03 2015

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

A043518 Numbers having two 7's in base 10.

Original entry on oeis.org

77, 177, 277, 377, 477, 577, 677, 707, 717, 727, 737, 747, 757, 767, 770, 771, 772, 773, 774, 775, 776, 778, 779, 787, 797, 877, 977, 1077, 1177, 1277, 1377, 1477, 1577, 1677, 1707, 1717, 1727, 1737, 1747, 1757, 1767, 1770, 1771

Offset: 1

Clark Kimberling

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

Subsequence of A011537.

Select[Range[2000],DigitCount[#,10,7]==2&] (* Harvey P. Dale, Jul 30 2022 *)

A043519 Numbers having three 7's in base 10.

Original entry on oeis.org

777, 1777, 2777, 3777, 4777, 5777, 6777, 7077, 7177, 7277, 7377, 7477, 7577, 7677, 7707, 7717, 7727, 7737, 7747, 7757, 7767, 7770, 7771, 7772, 7773, 7774, 7775, 7776, 7778, 7779, 7787, 7797, 7877, 7977, 8777, 9777, 10777

Offset: 1

Clark Kimberling

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

Subsequence of A011537.

Select[Range[11000],DigitCount[#,10,7]==3&] (* Harvey P. Dale, Mar 25 2015 *)

A043520 Numbers having four 7's in base 10.

Original entry on oeis.org

7777, 17777, 27777, 37777, 47777, 57777, 67777, 70777, 71777, 72777, 73777, 74777, 75777, 76777, 77077, 77177, 77277, 77377, 77477, 77577, 77677, 77707, 77717, 77727, 77737, 77747, 77757, 77767, 77770, 77771, 77772

Offset: 1

Clark Kimberling

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

Subsequence of A011537.

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

A285846 A039938 with duplicates removed.

Original entry on oeis.org

7, 37, 237, 1789, 4357, 14379, 19587, 93957, 189572, 189597, 1234397, 1839597, 1958798, 1983957, 3978594, 11983957, 19596487, 29195397, 39599197, 195991487, 339799143, 395991697, 1429199397, 1679895983, 1983994799, 2239951987, 11959939917, 15991995897

Offset: 1

J. Lowell, Apr 27 2017

Any proof that this sequence is infinite?

This sequence is infinite because A039938 is indeed infinite and for any number k there is a multiple of k which does not contain a '7', so A039938 contains infinitely many distinct terms. Both parts are easy to prove. - Giovanni Resta, Feb 26 2019

Giovanni Resta, Table of n, a(n) for n = 1..32

Cf. A039938.

Subsequence of A011537.

Union@ Table[SelectFirst[Range[10^6], Times @@ Boole@ Map[DigitCount[#, 10, 7] > 0 &, # Range@ n] > 0 &], {n, 12}] (* Michael De Vlieger, Apr 27 2017, Version 10 *)

a(19)-a(28) from Giovanni Resta, Apr 27 2017

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

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A257224 Numbers that have at least one divisor containing the digit 7 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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A257668 Primes containing a digit 7.

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A043518 Numbers having two 7's in base 10.

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A043519 Numbers having three 7's in base 10.

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A043520 Numbers having four 7's in base 10.

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

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