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 1-6 of 6 results.

A071955 a(n) = remainder when n is reduced mod reverse(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 13, 14, 15, 16, 17, 18, 19, 0, 9, 0, 23, 24, 25, 26, 27, 28, 29, 0, 5, 9, 0, 34, 35, 36, 37, 38, 39, 0, 13, 18, 9, 0, 45, 46, 47, 48, 49, 0, 6, 2, 18, 9, 0, 56, 57, 58, 59, 0, 13, 10, 27, 18, 9, 0, 67, 68, 69, 0, 3, 18, 36, 27, 18, 9, 0, 78, 79, 0, 9
Offset: 1

Views

Author

Joseph L. Pe, Jun 16 2002

Keywords

Comments

a(n)=0 if n is palindromic - Labos Elemer, Jan 28 2005

Examples

			a(85) = 85 mod 58 = 27.

Links

Crossrefs

Cf. A002113, A071590, A103164, A103168.

Programs

  • Mathematica
    Table[Mod[n, FromDigits[Reverse[IntegerDigits[n]]]], {n, 1, 256}] (* Labos Elemer, Jan 28 2005 *)
Table[Mod[n, FromDigits[Reverse[IntegerDigits[n]]]], {n, 1, 100}]
  • PARI
    a(n, base=10) = my (r=fromdigits(Vecrev(digits(n, base)), base)); n%r \\ Rémy Sigrist, Apr 05 2020

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jul 14 2007

A103167 a(n) = 2^n mod reverse(2^n).

Original entry on oeis.org

0, 0, 0, 16, 9, 18, 128, 256, 82, 1024, 2048, 4096, 2356, 16384, 32768, 1980, 131072, 262144, 524288, 1048576, 2097152, 159390, 319770, 16777216, 10108899, 20228688, 134217728, 268435456, 98713642, 1073741824, 2147483648, 4294967296, 2681134876, 17179869184
Offset: 1

Views

Author

Labos Elemer, Jan 28 2005

Keywords

Comments

Remainder if 2^n is divided by the reverse of 2^n.

Examples

			a(5) = 2^5 mod reverse(2^5) = 32 mod reverse(32) = 32 mod 23 = 9.

Links

Crossrefs

Cf. A002113, A071590, A103164-A103167.

Programs

  • Mathematica
    Table[Mod[FromDigits[Reverse[IntegerDigits[2^n]]], 2^n], {n, 1, 256}]
Table[PowerMod[2,n,IntegerReverse[2^n]],{n,40}] (* Harvey P. Dale, Jan 30 2022 *)
  • Python
    def a(n): t = 2**n; return t%int(str(t)[::-1])
print([a(n) for n in range(1, 35)]) # Michael S. Branicky, Dec 12 2021

A103166 a(n) = reverse(2^n) mod 2^n.

Original entry on oeis.org

0, 0, 0, 13, 23, 46, 53, 140, 215, 105, 210, 2808, 2918, 15593, 21187, 63556, 7987, 179118, 358137, 466945, 420750, 4034914, 8068838, 10946113, 23445533, 46880176, 22406063, 117663950, 219078635, 1060248229, 2021396468, 2632727628, 2954399858, 13837158803
Offset: 1

Views

Author

Labos Elemer, Jan 28 2005

Keywords

Comments

Remainder if (2^n written backwards) is divided by 2^n.

Examples

			a(4) = reverse(2^4) mod 2^4 = reverse(16) mod 16 = 61 mod 16 = 13.

Crossrefs

Cf. A002113, A071590, A103164-A103167.

Programs

  • Mathematica
    Table[Mod[FromDigits[Reverse[IntegerDigits[2^n]]], 2^n], {n, 1, 256}]
  • Python
    def a(n): t = 2**n; return int(str(t)[::-1])%t
print([a(n) for n in range(1, 35)]) # Michael S. Branicky, Dec 12 2021

A103390 Natural numbers but with nonprimes squared.

Original entry on oeis.org

0, 1, 2, 3, 16, 5, 36, 7, 64, 81, 100, 11, 144, 13, 196, 225, 256, 17, 324, 19, 400, 441, 484, 23, 576, 625, 676, 729, 784, 29, 900, 31, 1024, 1089, 1156, 1225, 1296, 37, 1444, 1521, 1600, 41, 1764, 43, 1936, 2025, 2116, 47, 2304, 2401, 2500, 2601, 2704, 53
Offset: 1

Views

Author

Parthasarathy Nambi, Mar 20 2005

Keywords

Examples

			4 is not a prime, so it is squared.

Links

Crossrefs

Cf. A103164.

Programs

  • Mathematica
    Table[ If[ PrimeQ[n], n, n^2], {n, 0, 54}] (* Robert G. Wilson v, Mar 24 2005 *)

Extensions

More terms from Robert G. Wilson v, Mar 24 2005

A282462 Integers but with the primes cubed.

Original entry on oeis.org

0, 1, 8, 27, 4, 125, 6, 343, 8, 9, 10, 1331, 12, 2197, 14, 15, 16, 4913, 18, 6859, 20, 21, 22, 12167, 24, 25, 26, 27, 28, 24389, 30, 29791, 32, 33, 34, 35, 36, 50653, 38, 39, 40, 68921, 42, 79507, 44, 45, 46, 103823, 48, 49, 50, 51, 52, 148877, 54, 55, 56
Offset: 0

Views

Author

Vincenzo Librandi, Feb 17 2017

Keywords

Examples

			a(4) = 4 because 4 is composite.
a(5) = 125 because 5 is prime and 5^3 = 125.

Links

Crossrefs

Cf. A061397, A103164, A143545.

Programs

  • Magma
    [0] cat [IsPrime(n) select n^3 else n: n in [1..60]];
  • Mathematica
    Join[{0},If[PrimeQ@#,#^3,#]&/@Range@80]

A380444 Sum of the nonprimes dividing n and the squares of the primes dividing n.

Original entry on oeis.org

1, 5, 10, 9, 26, 20, 50, 17, 19, 40, 122, 36, 170, 68, 50, 33, 290, 47, 362, 64, 80, 148, 530, 68, 51, 200, 46, 100, 842, 100, 962, 65, 164, 328, 110, 99, 1370, 404, 218, 112, 1682, 146, 1850, 196, 104, 580, 2210, 132, 99, 115, 350, 256, 2810, 128, 202, 164, 428, 904, 3482, 196, 3722, 1028, 152, 129, 260, 262, 4490, 400, 608, 208, 5042, 203, 5330, 1448, 150, 484
Offset: 1

Views

Author

Wesley Ivan Hurt, Jun 21 2025

Keywords

Comments

Inverse Möbius transform of A103164(n).

Examples

			a(12) = 1 + 2^2 + 3^2 + 4 + 6 + 12 = 36.

Crossrefs

Cf. A000005 (tau), A000203 (sigma), A005063, A008472 (sopf), A010051, A023890, A103164.

Programs

  • Mathematica
    Table[DivisorSigma[1, n] + Sum[p (p - 1), {p, Select[Divisors[n], PrimeQ]}], {n, 100}]

Formula

a(n) = sigma(n) - sopf(n) + sopf_2(n), where sopf_2(n) = Sum_{p|n, p prime} p^2.
a(n) = Sum_{d|n} d^tau(d^c(d)), where c = A010051.
a(n) = A023890(n) + A005063(n).
a(p^k) = (p^(k+1)+p^3-2*p^2+p-1)/(p-1) for p prime, k >= 1. - Wesley Ivan Hurt, Jul 02 2025
Showing 1-6 of 6 results.

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