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 1-3 of 3 results.

A242824 Primes formed by the initial digits of the decimal expansion of 1/7, starting at the first nonzero digit in the expansion.

Original entry on oeis.org

1428571, 1428571428571428571428571
Offset: 1

Views

Author

Felix Fröhlich, May 23 2014

Keywords

Comments

Next term has 355 digits.
All terms are of the form 6x+1; a(4) has 823 digits; and there are no further terms up to and including 10000 digits. - Harvey P. Dale, Oct 03 2018

Links

Crossrefs

Cf. A020806, A241217.
Corresponding sequences for 1/k: A093676 (k=12), A242826 (k=13), A242827 (k=14), A242828 (k=17), A242833 (k=19).

Programs

  • Mathematica
    Select[Table[FromDigits[PadRight[{},6n+1,{1,4,2,8,5,7}]],{n,200}],PrimeQ](* Harvey P. Dale, Oct 03 2018 *)

A343915 a(n) = floor(((n mod 6)+1) * 10^floor((n/6)+1) / 7).

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 14, 28, 42, 57, 71, 85, 142, 285, 428, 571, 714, 857, 1428, 2857, 4285, 5714, 7142, 8571, 14285, 28571, 42857, 57142, 71428, 85714, 142857, 285714, 428571, 571428, 714285, 857142, 1428571, 2857142, 4285714, 5714285, 7142857, 8571428, 14285714
Offset: 0

Views

Author

Konstantin Kutsenko, May 04 2021

Keywords

Comments

Every digit string (after the decimal point) in the decimal expansion of 1/7 = 0.142857142857142857... forms a term of this sequence.

Examples

			Every 6th term of the sequence starts with the same digits:
  1,        2,        4,        5,        7,        8,
  14,       28,       42,       57,       71,       85,
  142,      285,      428,      571,      714,      857,
  1428,     2857,     4285,     5714,     7142,     8571,
  14285,    28571,    42857,    57142,    71428,    85714,
  142857,   285714,   428571,   571428,   714285,   857142,
  1428571,  2857142,  4285714,  5714285,  7142857,  8571428,
  14285714, 28571428, 42857142, 57142857, 71428571, 85714285,
  ...

Links

Crossrefs

Cf. A020806, A241217, A343833.

Programs

  • PARI
    a(n) = {((n % 6)+1)*10^(n\6+1)\7} \\ Andrew Howroyd, May 05 2021

Formula

a(n) = floor(((n mod 6)+1) * 10^floor((n/6)+1) / 7).

A369562 Smallest positive n-digit number divisible by 7.

Original entry on oeis.org

7, 14, 105, 1001, 10003, 100002, 1000006, 10000004, 100000005, 1000000001, 10000000003, 100000000002, 1000000000006, 10000000000004, 100000000000005, 1000000000000001, 10000000000000003, 100000000000000002, 1000000000000000006, 10000000000000000004, 100000000000000000005
Offset: 1

Views

Author

J. Lowell, Jan 25 2024

Keywords

Comments

The only semiprime terms are a(2) = 14 and a(n) such that (10^(n-1) + 3)/7 is a prime. - Jon E. Schoenfield, Jan 27 2024

Examples

			a(3) = 105 = 7*15.

Links

Crossrefs

Cf. A033940, A241217, A369613.

Programs

  • Mathematica
    a[n_] := 10^(n - 1) + {6, 4, 5, 1, 3, 2}[[Mod[n, 6, 1]]]; Array[a, 30]
(* or *)
LinearRecurrence[{11, -10, -1, 11, -10}, {7, 14, 105, 1001, 10003, 100002}, 30] (* Amiram Eldar, Jan 27 2024 *)
Table[10^n+7-PowerMod[10,n,7],{n,0,20}] (* Harvey P. Dale, Jan 13 2025 *)

Formula

a(n) = (floor(10^(n-1)/7) + 1)*7.
a(n) = 10^(n-1) + A033940(n+2). - Amiram Eldar, Jan 27 2024
G.f.: 7*x*(1 - 9*x + 3*x^2 - x^3 - 3*x^4)/((1 - x)*(1 + x)*(1 - 10*x)*(1 - x + x^2)). - Stefano Spezia, Jan 28 2024
Showing 1-3 of 3 results.

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

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