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 11-15 of 15 results.

A082835 Decimal expansion of Kempner series Sum_{k >= 1, k has no digit 6 in base 10} 1/k.

Original entry on oeis.org

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

Views

Author

Robert G. Wilson v, Apr 14 2003

Keywords

Comments

Numbers with a digit 6 (A011536) have asymptotic density 1, i.e., here almost all terms are removed from the harmonic series, which makes convergence less surprising. See A082839 (the analog for digit 0) for more information about such so-called Kempner series. - M. F. Hasler, Jan 13 2020

Examples

			22.20559815955609188416738048000752710519385610666846327027693823... - _Robert G. Wilson v_, Jun 01 2009

References

  • Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 34.

Links

Crossrefs

Cf. A002387, A024101, A052414 (numbers with no '6'), A011536 (numbers with a '6').
Cf. A082830, A082831, A082832, A082833, A082834, A082836, A082837, A082838, A082839 (analog for digits 1, 2, 4, ..., 9 and 0).

Programs

  • Mathematica
    (* see the Mmca in Wolfram Library Archive. - Robert G. Wilson v, Jun 01 2009 *)

Formula

Equals Sum_{k in A052414\{0}} 1/k, where A052414 = numbers with no digit 6. - M. F. Hasler, Jan 15 2020

Extensions

Minor edits by M. F. Hasler, Jan 13 2020

A052411 Number of n-crossing hyperbolic knots having symmetry group Z1.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 2, 24, 173, 1047, 6709, 37177, 224311, 1301492
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

References

  • Hoste, J.; Thistlethwaite, M.; and Weeks, J. "The First 1,701,936 Knots." Math. Intell., 20, 33-48, Fall 1998.

Links

Crossrefs

Cf. A052411, A052412, A052413, A052414.

A052412 Number of n-crossing hyperbolic knots having symmetry group Z2.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 14, 57, 210, 712, 2268, 7011
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

References

  • Hoste, J.; Thistlethwaite, M.; and Weeks, J. "The First 1,701,936 Knots." Math. Intell., 20, 33-48, Fall 1998.

Links

Crossrefs

Cf. A052411, A052412, A052413, A052414.

A104426 Numbers k such that the digit 6 does not appear in the decimal expansion of k, Pk, Pk+k, Pk-k, or Pk*k, where Pk is the k-th prime.

Original entry on oeis.org

1, 3, 4, 7, 8, 9, 10, 11, 12, 13, 20, 21, 22, 25, 30, 33, 35, 37, 41, 43, 44, 48, 50, 51, 52, 53, 54, 55, 58, 70, 72, 75, 80, 81, 82, 83, 85, 93, 95, 128, 149, 152, 170, 171, 174, 184, 185, 187, 188, 189, 194, 198, 201, 203, 210, 212, 215, 217, 233, 235, 238, 242, 245
Offset: 1

Views

Author

Zak Seidov, Mar 07 2005

Keywords

Comments

From the first 3000 primes, only 179 are terms.
From the first 3000 integers, only 343 are terms.

Crossrefs

Cf. A052414, A104419, A104420, A104421, A104422, A104423, A104424, A104425, A104427, A104428.

Programs

  • Mathematica
    id[x_]:=IntegerDigits[x];pr[i_]:=Prime[i];ra=Range[3000];A104426=Select[ra, Position[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]], 6]=={}&]
slQ[n_]:=Module[{p=Prime[n]},Union[DigitCount[#,10,6]&/@{n,p,p+n,p-n, p*n}] == {0}]; Select[Range[250],slQ] (* Harvey P. Dale, Feb 01 2018 *)
  • PARI
    has(n)=!setsearch(Set(digits(n)),6)
is(n,p=prime(n))=has(n) && has(p) && has(p+n) && has(p-n) && has(p*n) \\ Charles R Greathouse IV, Feb 01 2018

Extensions

Definition modified (at the suggestion of N. J. A. Sloane) by Harvey P. Dale, Feb 10 2018

A338287 Decimal expansion of the sum of reciprocals of the numbers that are not pandigital numbers (version 2, A171102).

Original entry on oeis.org

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

Views

Author

Amiram Eldar, Oct 20 2020

Keywords

Comments

The sum of the reciprocals of the terms of the complement of A171102: numbers with at most 9 distinct digits. It is the union of the 10 sequences of numbers without a single given digit (see the Crossrefs section).
The terms in the data section were taken from the 200 decimal digits given by Strich and Müller (2020).

Examples

			65.74331110185328196734583167680868411685344106635398...

Links

  • Robert Strich and Eric Müller, Ziffernreduzierte Zahlen, in: E. Specht, E. Quaisser and P. Bauermann (eds.), 50 Jahre Bundeswettbewerb Mathematik, Springer Spektrum, Berlin, Heidelberg, 2020, pp. 171-182.

Crossrefs

Cf. A171102, A179954, A082830, A082831, A082832, A082833, A082834, A082835, A082836, A082837, A082838, A082839.
Cf. A052382 (numbers without the digit 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).

Formula

Equals 1/1 + 1/2 + 1/3 + ... + 1/1023456788 + 1/1023456790 + ..., i.e., A171102(1) = 1023456789 is the first number whose reciprocal is not in the sum.
Previous Showing 11-15 of 15 results.

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

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