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.

A096507 Numbers k such that 6*R_k + 1 is a prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

1, 2, 6, 8, 9, 11, 20, 23, 41, 63, 66, 119, 122, 149, 252, 284, 305, 592, 746, 875, 1204, 1364, 2240, 2403, 5106, 5776, 5813, 12456, 14235, 39606, 55544, 84239, 275922
Offset: 1

Views

Author

Labos Elemer, Jul 12 2004

Keywords

Comments

Also numbers k such that (2*10^k + 1)/3 is prime.
These numbers form a near-repdigit sequence (6)w7.
All the terms from k = 2403 through 14235 correspond to primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Oct 03 2005

Examples

			k = 9 gives 2000000001/3 = 666666667, which is prime.
k = 20 gives 66666666666666666667, which is prime.

Links

Crossrefs

Cf. A002275, A056657, A093170, A096503, A096504, A096505, A096506, A096508.

Programs

  • Mathematica
    Select[Range@ 2500, PrimeQ[FromDigits@ Table[6, {#}] + 1] &] (* or *)
Select[Range@ 2500, PrimeQ[2 (10^# - 1)/3 + 1] &] (* Michael De Vlieger, Jul 04 2016 *)

Formula

a(n) = A056657(n) + 1.

Extensions

More terms from Julien Peter Benney (jpbenney(AT)ftml.net), Sep 14 2004
39606 and 55544 from Serge Batalov, Jun 2009
84239 from Serge Batalov, Jul 06 2009 confirmed as next term by Ray Chandler, Feb 23 2012
a(33) from Kamada data by Tyler Busby, Apr 14 2024

A096506 Numbers n for which 2*R_n + 1 is a prime, where R_n = 11...1 is the repunit (A002275) of length n.

Original entry on oeis.org

1, 2, 3, 8, 11, 36, 95, 101, 128, 260, 351, 467, 645, 1011, 1178, 1217, 2442, 3761, 3806, 15617, 26459, 63117, 88545, 93497
Offset: 1

Views

Author

Labos Elemer, Jul 12 2004

Keywords

Comments

Also numbers n such that (2*10^n + 7)/9 is prime.
Per Kamada link, 181457, 202059, 262874 are also terms, found by Rytis Slatkevicius. - Michael S. Branicky, Sep 13 2024

Examples

			n=36: 222222222222222222222222222222222223 is a prime number.

Links

Crossrefs

Cf. A056656, A093162, A096503, A096504, A096505, A096507, A096508.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ 2(10^n - 1)/9 + 1], Print[n]], {n, 7000}] (* Robert G. Wilson v, Oct 14 2004 *)

Formula

a(n) = A056656(n) + 1.

Extensions

a(20)-a(24) from Kamada link by Ray Chandler, Feb 27 2012

A096504 Euler-phi applied to A096503 results in these decimal repdigits.

Original entry on oeis.org

1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 4, 6, 8, 8, 6, 8, 22, 8, 8, 22, 66, 44, 88, 44, 88, 66, 44, 88, 88, 222, 88, 88, 222, 444, 444, 888, 888, 444, 888, 888, 888, 888, 888, 888, 444444, 666666, 444444, 888888, 888888, 666666, 888888, 888888, 888888, 888888, 888888
Offset: 1

Views

Author

Labos Elemer, Jul 12 2004

Keywords

Examples

			a(60) = A000010(A096503(60)) = A000010(88888892) = 44444444.
Regular solutions: if p = repdigit + 1 is prime, then phi(p) = repdigit.

Links

Crossrefs

Cf. A000010, A010785, A096503, A096505.

Programs

  • PARI
    lista(nn) = {for (n= 1, nn, phin = eulerphi(n); d = digits(e=eulerphi(n)); if (vecmin(d) == vecmax(d), print1(e, ", ")););} \\ Michel Marcus, Sep 07 2014

Formula

a(n) = A000010(A096503(n)).
Showing 1-3 of 3 results.

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

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