cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A062679 Numbers such that every divisor (except 1, but including the number itself) contains the digit 9.

Original entry on oeis.org

19, 29, 59, 79, 89, 97, 109, 139, 149, 179, 191, 193, 197, 199, 229, 239, 269, 293, 349, 359, 379, 389, 397, 409, 419, 439, 449, 479, 491, 499, 509, 569, 593, 599, 619, 659, 691, 709, 719, 739, 769, 797, 809, 829, 839, 859, 907, 911, 919, 929, 937, 941, 947
Offset: 1

Views

Author

Erich Friedman, Jul 04 2001

Keywords

Comments

Different from A106093. 1691 = 19 * 89 is the smallest term that is not in A106093. - Franklin T. Adams-Watters, Apr 30 2007

Examples

			7961 has divisors 19, 419 and 7961, all of which contain the digit 9.

Links

Crossrefs

Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062680.

Programs

  • Magma
    [n: n in [2..1000] | forall{Divisors(n)[i]: i in [2..NumberOfDivisors(n)] | 9 in Intseq(Divisors(n)[i])}]; // Bruno Berselli, Nov 21 2015
  • Mathematica
    fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1000], fQ[#, 9] &] (* Robert G. Wilson v, Jun 11 2014 *)
d9Q[n_]:=First[Union[DigitCount[#,10,9]&/@Rest[Divisors[n]]]]>0; Select[ Range[ 2,1000],d9Q] (* Harvey P. Dale, Sep 12 2014 *)
  • PARI
    isok(n) = {if (n==1, return (0)); d = divisors(n); for (k=1, #d, if ((d[k] != 1) && (vecmax(digits(d[k])) != 9), return (0));); return (1);} \\ Michel Marcus, Nov 21 2015

A106100 Primes with maximal digit = 2.

Original entry on oeis.org

2, 211, 1021, 1201, 2011, 2111, 2221, 10211, 12011, 12101, 12211, 20011, 20021, 20101, 20201, 21001, 21011, 21101, 21121, 21211, 21221, 22111, 101021, 101221, 102001, 102101, 102121, 110221, 111121, 111211, 112111, 112121, 120011, 120121
Offset: 1

Views

Author

Zak Seidov, May 07 2005

Keywords

Comments

Subsequence of A036953. Prime numbers p such that A209928(p) = 2. Complement of A221698 with respect to A221697. [Jaroslav Krizek, Jan 22 2013]

Links

Crossrefs

Cf. A106093, A106094, A106095, A106096, A106097, A106098, A106099.

Programs

  • Maple
    N:= 6: # to get all terms of up to N digits
M2:= {1};M1:= {1}:
for d from 1 to N-1 do
  M2:= map(t -> (t, t+10^d, t+2*10^d), M2);
  M1:= map(t -> (t, t+10^d), M1);
od:
sort(convert({2} union select(isprime,M2 minus M1),list)); # Robert Israel, Jun 19 2016
  • Mathematica
    Select[Prime[Range[10000]], Max[IntegerDigits[ # ]]==2&]
  • PARI
    isok(p) = isprime(p) && (vecmax(digits(p)) == 2); \\ Michel Marcus, Jan 02 2019

Extensions

More terms from Rick L. Shepherd, May 22 2005

A106099 Primes with maximal digit = 3.

Original entry on oeis.org

3, 13, 23, 31, 103, 113, 131, 223, 233, 311, 313, 331, 1013, 1031, 1033, 1103, 1123, 1213, 1223, 1231, 1301, 1303, 1321, 2003, 2113, 2131, 2203, 2213, 2311, 2333, 3001, 3011, 3023, 3121, 3203, 3221, 3301, 3313, 3323, 3331
Offset: 1

Views

Author

Zak Seidov, May 07 2005

Keywords

Links

Crossrefs

Cf. A106093, A106094, A106095, A106096, A106097, A106098, A106100.

Programs

  • Maple
    Res:= 3: count:= 1:
A:= {3}: B:= {$1..2}:
for d from 2 while count < 100 do
  A:= {seq(seq(10*a+i,i=0..3),a=A), seq(10*b+3,b=B)}:
  B:= {seq(seq(10*b+i,i=0..2),b=B)}:
  S:= sort(convert(select(isprime,A),list));
  count:= count + nops(S);
  Res:= Res, op(S);
od:
Res; # Robert Israel, Jan 01 2019
  • Mathematica
    Select[Prime[Range[600]], Max[IntegerDigits[ # ]]==3&]

A106097 Primes with maximal digit = 5.

Original entry on oeis.org

5, 53, 151, 251, 353, 503, 521, 523, 541, 1051, 1151, 1153, 1451, 1453, 1511, 1523, 1531, 1543, 1553, 2053, 2153, 2251, 2351, 2503, 2521, 2531, 2543, 2551, 3251, 3253, 3511, 3533, 3541
Offset: 1

Views

Author

Zak Seidov, May 07 2005

Keywords

Links

Crossrefs

Cf. A106100, A106099, A106098, A106096, A106095, A106094, A106093.

Programs

  • Mathematica
    Select[Prime[Range[500]], Max[IntegerDigits[ # ]]==5&]

A106098 Primes with maximal digit = 4.

Original entry on oeis.org

41, 43, 241, 401, 421, 431, 433, 443, 1423, 1433, 2141, 2143, 2243, 2341, 2411, 2423, 2441, 3041, 3343, 3413, 3433, 4001, 4003, 4013, 4021, 4111, 4133, 4201, 4211, 4231, 4241, 4243
Offset: 1

Views

Author

Zak Seidov, May 07 2005

Keywords

Links

Crossrefs

Cf. A106100, A106099, A106097, A106096, A106095, A106094, A106093.

Programs

  • Mathematica
    Select[Prime[Range[600]], Max[IntegerDigits[ # ]]==4&]

A284290 Primes containing a digit 4.

Original entry on oeis.org

41, 43, 47, 149, 241, 347, 349, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 541, 547, 641, 643, 647, 743, 941, 947, 1049, 1249, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489
Offset: 1

Views

Author

Jaroslav Krizek, Mar 24 2017

Keywords

Comments

Subsequence of A011534 and A062669.

Links

Crossrefs

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), A284292 (k = 8), A106093 (k = 9).

Programs

  • Magma
    [p: p in PrimesUpTo(10000) | 4 in Intseq(p)]
  • Mathematica
    Select[Range[1500], PrimeQ[#] && MemberQ[IntegerDigits[#], 4] &] (* Amiram Eldar, Nov 09 2019 *)

A284291 Primes containing a digit 6.

Original entry on oeis.org

61, 67, 163, 167, 263, 269, 367, 461, 463, 467, 563, 569, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 761, 769, 863, 967, 1061, 1063, 1069, 1163, 1361, 1367, 1567, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663
Offset: 1

Views

Author

Jaroslav Krizek, Mar 24 2017

Keywords

Comments

Subsequence of A011536 and A062673.

Links

Crossrefs

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), A284292 (k = 8), A106093 (k = 9).

Programs

  • Magma
    [p: p in PrimesUpTo(10000) | 6 in Intseq(p)];
  • Mathematica
    Select[Range[2000], PrimeQ[#] && MemberQ[IntegerDigits[#], 6] &] (* Amiram Eldar, Nov 09 2019 *)

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

Views

Author

Jaroslav Krizek, Mar 25 2017

Keywords

Comments

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

Links

Crossrefs

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).

Programs

  • Magma
    [p: p in PrimesUpTo(10000) | 8 in Intseq(p)];
  • Maple
    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
  • Mathematica
    Select[Prime@ Range@ 500, MemberQ[ IntegerDigits@ #, 8] &] (* Giovanni Resta, Mar 25 2017 *)
  • Python
    from sympy import primerange
print([n for n in primerange(2, 2000) if '8' in str(n)]) # Indranil Ghosh, Mar 25 2017
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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