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.

Previous Showing 11-16 of 16 results.

A353439 Integers m such that the decimal expansion of 1/m contains the digit 3.

Original entry on oeis.org

3, 12, 13, 17, 19, 23, 26, 27, 28, 29, 30, 31, 32, 33, 34, 38, 41, 42, 43, 46, 47, 48, 49, 51, 52, 53, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 81, 83, 85, 87, 88, 89, 92, 93, 94, 95, 97, 98, 102, 103, 104, 105, 106, 107, 109, 113, 114, 115, 116
Offset: 1

Views

Author

Bernard Schott and Robert G. Wilson v, Apr 22 2022

Keywords

Comments

If m is a term, 10*m is also a term, so terms with no trailing zeros are all primitive terms.

Examples

			m = 12 is a term since 1/12 = 0.083333333333... (here, 3 is the smallest digit).
m = 13 is a term since 1/13 = 0.076923076923...
m = 75 is a term since 1/15 = 0.013333333333... (here, 3 is the largest digit).

Crossrefs

A350814 (largest digit=3) and A352157 (smallest digit=3) are subsequences.
Similar with digit k: A352154 (k=0), A353437 (k=1), A353438 (k=2), this sequence (k=3), A353440 (k=4), A353441 (k=5), A353442 (k=6), A353443 (k=7), A353444 (k=8), A333237 (k=9).

Programs

  • Mathematica
    f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 125, MemberQ[f@#, 3] &]

A353440 Integers m such that the decimal expansion of 1/m contains the digit 4.

Original entry on oeis.org

7, 14, 17, 19, 21, 22, 23, 24, 25, 26, 28, 29, 31, 34, 35, 38, 39, 41, 43, 46, 47, 49, 51, 53, 56, 57, 58, 59, 61, 62, 65, 67, 68, 69, 70, 71, 76, 79, 81, 83, 84, 85, 86, 87, 89, 92, 93, 94, 95, 96, 97, 98, 102, 103, 104, 106, 107, 109, 112, 113, 114, 115, 116, 117, 118
Offset: 1

Views

Author

Bernard Schott and Robert G. Wilson v, Apr 24 2022

Keywords

Comments

If m is a term, 10*m is also a term, so terms with no trailing zeros are all primitive terms.

Examples

			m = 14 is a term since 1/14 = 0.0714285714285...
m = 22 is a term since 1/22 = 0.04545454545... (here, 4 is the smallest digit).
m = 693 is a term since 1/693 = 0.001443001443... (here, 4 is the largest digit).

Links

Crossrefs

A351470 (largest digit=4) and A352158 (smallest digit=4) are subsequences.
Similar with digit k: A352154 (k=0), A353437 (k=1), A353438 (k=2), A353439 (k=3), this sequence (k=4), A353441 (k=5), A353442 (k=6), A353443 (k=7), A353444 (k=8), A333237 (k=9).

Programs

  • Mathematica
    f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 125, MemberQ[f@#, 4] &]

A353442 Integers m such that the decimal expansion of 1/m contains the digit 6.

Original entry on oeis.org

6, 13, 15, 16, 17, 19, 21, 23, 24, 26, 29, 31, 34, 38, 39, 46, 47, 49, 51, 52, 53, 57, 58, 59, 60, 61, 62, 64, 65, 68, 69, 71, 73, 76, 79, 81, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 102, 103, 104, 106, 107, 109, 113, 114, 115, 116, 118, 119, 121, 122, 124, 126
Offset: 1

Views

Author

Bernard Schott and Robert G. Wilson v, Apr 25 2022

Keywords

Comments

If m is a term, 10*m is also a term, so terms with no trailing zeros are all primitive terms.

Examples

			m = 6 is a term since 1/6 = 0.16666666666...
m = 13 is a term since 1/13 = 0.076923076923...
m = 103125 is a term since 1/103125 = 0.00000969696...

Links

Crossrefs

A351472 (largest digit=6) and A352160 (smallest digit=6) are subsequences.
Similar with digit k: A352154 (k=0), A353437 (k=1), A353438 (k=2), A353439 (k=3), A353440 (k=4), A353441 (k=5), this sequence (k=6), A353443 (k=7), A353444 (k=8), A333237 (k=9).

Programs

  • Mathematica
    f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 150, MemberQ[f@#, 6] &]

A353443 Integers m such that the decimal expansion of 1/m contains the digit 7.

Original entry on oeis.org

7, 13, 14, 17, 19, 21, 23, 27, 28, 29, 34, 35, 36, 37, 38, 43, 44, 46, 47, 49, 51, 52, 53, 56, 57, 58, 59, 61, 63, 67, 68, 69, 70, 71, 76, 77, 79, 81, 83, 84, 85, 86, 87, 89, 92, 93, 94, 95, 97, 98, 102, 103, 107, 109, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 126, 127
Offset: 1

Views

Author

Bernard Schott and Robert G. Wilson v, Apr 25 2022

Keywords

Comments

If m is a term, 10*m is also a term, so terms with no trailing zeros are all primitive terms.

Examples

			m = 7 is a term since 1/7 = 0.142857142857...
m = 27 is a term since 1/27 = 0.037037037... (here, 7 is the largest digit).

Links

Crossrefs

A351473 (largest digit=7) is a subsequence.
Similar with digit k: A352154 (k=0), A353437 (k=1), A353438 (k=2), A353439 (k=3), A353440 (k=4), A353441 (k=5), A353442 (k=6), this sequence (k=7), A353444 (k=8), A333237 (k=9).

Programs

  • Mathematica
    f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 150, MemberQ[f@#, 7] &]

A353444 Integers m such that the decimal expansion of 1/m contains the digit 8.

Original entry on oeis.org

7, 12, 14, 17, 19, 23, 26, 28, 29, 31, 34, 35, 38, 42, 43, 46, 47, 48, 49, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 70, 71, 72, 73, 76, 77, 78, 79, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 98, 102, 103, 104, 105, 107, 109, 112, 113, 114, 115, 116, 117, 118
Offset: 1

Views

Author

Bernard Schott and Robert G. Wilson v, Apr 25 2022

Keywords

Comments

If m is a term, 10*m is also a term, so terms with no trailing zeros are all primitive terms.

Examples

			m = 12 is a term since 1/12 = 0.08333333333...
m = 17 is a term since 1/17 = 0.05882352941176470588235294117647...
m = 125 is a term since 1/125 = 0.008.

Links

Crossrefs

A351474 (largest digit=8) and A352161 (smallest digit=8) are subsequences.
Similar with digit k: A352154 (k=0), A353437 (k=1), A353438 (k=2), A353439 (k=3), A353440 (k=4), A353441 (k=5), A353442 (k=6), A353443 (k=7), this sequence (k=8), A333237 (k=9).

Programs

  • Mathematica
    f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 150, MemberQ[f@#, 8] &]
Select[Range[150],MemberQ[realDigitsRecip[#],8]&] (* The realDigitsRecip program is at A021200 *) (* Harvey P. Dale, Jan 11 2025 *)

A362710 Numbers m such that the decimal expansion of 1/m contains no digit 0, ignoring leading and trailing 0's.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, 24, 25, 26, 28, 30, 32, 35, 36, 40, 44, 45, 50, 54, 55, 56, 60, 64, 65, 66, 70, 72, 74, 75, 80, 82, 88, 90, 100, 104, 108, 112, 120, 125, 128, 132, 140, 144, 148, 150, 160, 175, 176, 180, 200, 216, 220, 224, 225, 240, 250, 252, 260, 264
Offset: 1

Views

Author

Robert Israel, Apr 30 2023

Keywords

Comments

If k is a term, then so is 10*k.

Examples

			a(12) = 14 is a term because 1/14 = 0.0714285714... contains no digit 0 except for leading 0's.

Links

Crossrefs

Complement of A352154. Cf. A362579.

Programs

  • Maple
    removeInitial0:= proc(L) local i;
  for i from 1 to nops(L) do if L[i] <> 0 then return L[i..-1] fi od;
  []
end proc:
filter:= proc(n) local q;
  q:= NumberTheory:-RepeatingDecimal(1/n);
  not(member(0, removeInitial0(NonRepeatingPart(q))) or member(0, RepeatingPart(q)))
end proc:
select(filter, [$1..300]);
  • Mathematica
    Select[Range[500], FreeQ[First[RealDigits[1/#]], 0] &] (* Paolo Xausa, Apr 22 2024 *)
  • Python
    from itertools import count, islice
from sympy import multiplicity, n_order
def A362710_gen(startvalue=1): # generator of terms >= startvalue
    for a in count(max(startvalue,1)):
        m2, m5 = (~a&a-1).bit_length(), multiplicity(5,a)
        k, m = 10**max(m2,m5), 10**(t:=n_order(10,a//(1<A362710_list = list(islice(A362710_gen(),30)) # Chai Wah Wu, May 04 2023
Previous Showing 11-16 of 16 results.

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