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 1-10 of 72 results. Next

A317824 a(n) = A000422(n)^^A000422(n) (mod 10^len(A000422(n))), where ^^ indicates tetration or hyper-4 (e.g., 3^^4 = 3^(3^(3^3))).

Original entry on oeis.org

1, 21, 721, 8721, 8721, 708721, 5708721, 65708721, 165708721, 65165708721, 1165165708721, 861165165708721, 5861165165708721, 5005861165165708721, 55005861165165708721, 48055005861165165708721, 8448055005861165165708721, 388448055005861165165708721, 49388448055005861165165708721
Offset: 1

Views

Author

Marco Ripà, Aug 10 2018

Keywords

Comments

For any n, a(n) (mod 10^len(A000422(n))) == a(n + 1) (mod 10^len(A000422(n))), where len(k) := number of digits in k. Assuming len(a(n))>1, this is a general property of every concatenated sequence with fixed rightmost digits (such as A061839 or A014925), as shown in Ripà's book "La strana coda della serie n^n^...^n".

Examples

			For n = 3, a(3) = 321^^321 (mod 10^3) = 721. In fact, a(3) (mod 10^3) == a(4) (mod 10^3), since 721 (mod 10^3) == 8721 (mod 10^3).

References

  • Marco Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, page 60. ISBN 978-88-6178-789-6

Links

Crossrefs

Cf. A000422, A058183, A171882 (tetration), A317903.

Programs

  • PARI
    tmod(b, n) = {if (b % n == 0, return (0)); if (b % n == 1, return (1)); if (gcd(b, n)==1, return (lift(Mod(b, n)^tmod(b, lift(znorder(Mod(b, n))))))); lift(Mod(b, n)^(eulerphi(n) + tmod(b, eulerphi(n))));}
f(n) = my(t=n); forstep(k=n-1, 1, -1, t=t*10^#Str(k)+k); t; \\ A000422
a(n) = my(x=f(n)); tmod(x, 10^#Str(x)); \\ Michel Marcus, Sep 12 2021

Formula

a(n) = (n_n-1_n-2_...2_1)^^(n_n-1_n-2...2_1) (mod 10^len(n_n-1_n-2..._2_1)), where len(k) := number of digits in k.

Extensions

More terms from Jinyuan Wang, Aug 30 2020

A353110 Binary representation of A000422(n).

Original entry on oeis.org

1, 10101, 101000001, 1000011100001, 1101010000110001, 10011111101111110001, 11101001100101110110001, 101001110010111111110110001, 111010110111100110100010110001, 1010001110111010100100110010110001
Offset: 1

Views

Author

Seiichi Manyama, Apr 24 2022

Keywords

Crossrefs

Cf. A000422, A353111, A353112, A353113, A353114, A353115, A353116, A353117.
Cf. A007088, A050926.

Programs

  • Ruby
    def A(k, n)
  (1..n).map{|i| (1..i).to_a.reverse.join.to_i.to_s(k).to_i}
end
p A(2, 10)

Formula

a(n) = A007088(A000422(n)).

A353111 Base-3 representation of A000422(n).

Original entry on oeis.org

1, 210, 102220, 12221001, 2202111220, 1020020120010, 112101212202101, 20002221022010100, 2112211110001000200, 1001100202012200011001, 10221012122122021102212210, 120212211002121222001110211020, 2100201122222221220212010020220201
Offset: 1

Views

Author

Seiichi Manyama, Apr 24 2022

Keywords

Crossrefs

Cf. A000422, A353110, A353112, A353113, A353114, A353115, A353116, A353117.
Cf. A007089, A097580.

Programs

  • Ruby
    def A(k, n)
  (1..n).map{|i| (1..i).to_a.reverse.join.to_i.to_s(k).to_i}
end
p A(3, 20)

Formula

a(n) = A007089(A000422(n)).

A353112 Base-4 representation of A000422(n).

Original entry on oeis.org

1, 111, 11001, 1003201, 31100301, 2133233301, 131030232301, 11032113332301, 322313212202301, 22032322210302301, 100022230001210102301, 123202121121121130102301, 232213121102313132210102301, 1032130122202213111001210102301
Offset: 1

Views

Author

Seiichi Manyama, Apr 24 2022

Keywords

Crossrefs

Cf. A000422, A353110, A353111, A353113, A353114, A353115, A353116, A353117.
Cf. A007090, A353104.

Programs

  • Ruby
    def A(k, n)
  (1..n).map{|i| (1..i).to_a.reverse.join.to_i.to_s(k).to_i}
end
p A(4, 20)

Formula

a(n) = A007090(A000422(n)).

A353113 Base-5 representation of A000422(n).

Original entry on oeis.org

1, 41, 2241, 114241, 3214241, 131414241, 3424414241, 134414414241, 4010314414241, 140000314414241, 121200300314414241, 111333240300314414241, 102224302240300314414241, 43323231102240300314414241, 40130121131102240300314414241
Offset: 1

Views

Author

Seiichi Manyama, Apr 24 2022

Keywords

Crossrefs

Cf. A000422, A353110, A353111, A353112, A353114, A353115, A353116, A353117.
Cf. A007091, A353105.

Programs

  • Ruby
    def A(k, n)
  (1..n).map{|i| (1..i).to_a.reverse.join.to_i.to_s(k).to_i}
end
p A(5, 20)

Formula

a(n) = A007091(A000422(n)).

A353114 Base-6 representation of A000422(n).

Original entry on oeis.org

1, 33, 1253, 32001, 1055253, 22005133, 432020401, 12410423013, 242000505413, 5014143322001, 2210214121042333, 1105325341502010053, 333110135101300035201, 144230053432212010304453, 51542110115212012113433133
Offset: 1

Views

Author

Seiichi Manyama, Apr 24 2022

Keywords

Crossrefs

Cf. A000422, A353110, A353111, A353112, A353113, A353115, A353116, A353117.
Cf. A007092, A353106.

Programs

  • Ruby
    def A(k, n)
  (1..n).map{|i| (1..i).to_a.reverse.join.to_i.to_s(k).to_i}
end
p A(6, 20)

Formula

a(n) = A007092(A000422(n)).

A353115 Base-7 representation of A000422(n).

Original entry on oeis.org

1, 30, 636, 15412, 314241, 5363433, 122026543, 2113022646, 33321631443, 536166343420, 143160211151106, 34336660114345260, 11025520662032415631, 2346534662055361221261, 535040660151320030232114, 150206616416004416563301662
Offset: 1

Views

Author

Seiichi Manyama, Apr 24 2022

Keywords

Crossrefs

Cf. A000422, A353110, A353111, A353112, A353113, A353114, A353116, A353117.
Cf. A007093, A097582.

Programs

  • Ruby
    def A(k, n)
  (1..n).map{|i| (1..i).to_a.reverse.join.to_i.to_s(k).to_i}
end
p A(7, 20)

Formula

a(n) = A007093(A000422(n)).

A353116 Base-8 representation of A000422(n).

Original entry on oeis.org

1, 25, 501, 10341, 152061, 2375761, 35145661, 516277661, 7267464261, 121672446261, 20125401442261, 3342313131342261, 564731226736442261, 116343242472501442261, 20325073566675147442261, 3327107422474572347442261
Offset: 1

Views

Author

Seiichi Manyama, Apr 24 2022

Keywords

Crossrefs

Cf. A000422, A353110, A353111, A353112, A353113, A353114, A353115, A353117.
Cf. A007094, A097583.

Programs

  • Ruby
    def A(k, n)
  (1..n).map{|i| (1..i).to_a.reverse.join.to_i.to_s(k).to_i}
end
p A(8, 20)

Formula

a(n) = A007094(A000422(n)).

A353117 Base-9 representation of A000422(n).

Original entry on oeis.org

1, 23, 386, 5831, 82456, 1206503, 15355671, 202838110, 2484401020, 31322180131, 3835578242783, 525732558043736, 70648887825106821, 10365384555277543376, 1340704717754261643863, 173544168713353406577421
Offset: 1

Views

Author

Seiichi Manyama, Apr 24 2022

Keywords

Crossrefs

Cf. A000422, A353110, A353111, A353112, A353113, A353114, A353115, A353116.
Cf. A007095, A353107.

Programs

  • Ruby
    def A(k, n)
  (1..n).map{|i| (1..i).to_a.reverse.join.to_i.to_s(k).to_i}
end
p A(9, 20)

Formula

a(n) = A007095(A000422(n)).

A176024 Numbers k such that the reverse concatenation of the first k integers (A000422(k)) is a prime.

Original entry on oeis.org

82, 37765
Offset: 1

Views

Author

Eric W. Weisstein, Apr 06 2010

Keywords

Comments

a(1) was pointed out by Artur Jasinski, Mar 30 2008 (see A000422).
a(2) was found by Eric W. Weisstein, Apr 06 2010.
a(3) > 84300. - Tyler Busby, Feb 21 2023

Examples

			a(1) is 82 since the 155-digit number 828180...54321 is prime.
a(2) is 37765 since the 177719-digit number 377653776437763...54321 is (a probable) prime.

Links

Crossrefs

Cf. A000422, A007908, A176942.

Extensions

Edited by N. J. A. Sloane, Dec 03 2021
Showing 1-10 of 72 results. Next

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

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