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 1-4 of 4 results.

A134656 Corresponding GCD values in A116894.

Original entry on oeis.org

2, 10453, 129341, 157519, 555097, 595411, 624363411431
Offset: 1

Views

Author

Ryan Propper, Feb 01 2008

Keywords

Crossrefs

Cf. A116894.

Programs

  • C
    // See Links section in A116893.
  • PARI
    for(n = 1, 10^9, my(x = gcd(n! + 1, n^n + 1)); if(x != 1 && x != 2*n + 1, print1(x, ", ")))
    

Formula

a(n) = gcd(A116894(n)! + 1, A116894(n)^A116894(n) + 1)

Extensions

a(6)-a(7) from Nick Hobson, Feb 20 2024

A116893 Numbers k such that gcd(k!+1, k^k+1) > 1.

Original entry on oeis.org

1, 3, 23, 39, 51, 63, 95, 99, 131, 183, 191, 215, 239, 251, 299, 303, 315, 363, 371, 411, 419, 431, 443, 495, 543, 575, 659, 683, 711, 743, 755, 791, 831, 891, 911, 935, 975, 1019, 1031, 1055, 1071, 1143, 1155, 1191, 1211, 1223, 1251, 1275, 1295, 1355
Offset: 1

Views

Author

Giovanni Resta, Mar 01 2006

Keywords

Comments

See A116892 for the corresponding values of the GCD. See also comments in A116891.

Examples

			gcd(1!+1, 1^1+1) = 2, gcd(2!+1, 2^2+1) = 1 and gcd(3!+1, 3^3+1) = 7, so 1 and 3 are the first two terms of the sequence.
		

Crossrefs

Programs

  • C
    See Links section.
  • Mathematica
    Select[Range[1500], (GCD[ #!+1, #^#+1] > 1)&]
  • PARI
    isok(n) = gcd(n! + 1, n^n + 1) != 1; \\ Michel Marcus, Jul 22 2018
    

A116891 a(n) = gcd(n! + 1, n^n + 1).

Original entry on oeis.org

2, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 47, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 79, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 103, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 127, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 191, 1, 1, 1, 199, 1, 1
Offset: 1

Views

Author

Giovanni Resta, Mar 01 2006

Keywords

Comments

Apparently all the values greater than 1 (cf. A116892) are prime numbers and are equal to 2n+1 with only 4 exceptions for n<82000 (cf. A116894).
From Antti Karttunen, Jul 22 2018: (Start)
The first duplicated value > 1 is 157519 = a(43755) = a(78759). Note that 43755 = 15*2917, while 78759 = 27*2917.
It seems that for the long time after a(1) = 2, all other terms > 1 occur only at such positions k that k+1 is not squarefree. However, this turns out to be false as a(208161) = 555097, and 208162 is a squarefree number.
(End)

Examples

			a(3) = gcd(3! + 1, 3^3 + 1) = gcd(7,28) = 7.
		

Crossrefs

Programs

A116892 Values of gcd(k!+1, k^k+1), when greater than 1.

Original entry on oeis.org

2, 7, 47, 79, 103, 127, 191, 199, 263, 367, 383, 431, 479, 503, 599, 607, 631, 727, 743, 823, 839, 863, 887, 991, 1087, 1151, 1319, 1367, 1423, 1487, 1511, 1583, 1663, 1783, 1823, 1871, 1951, 2039, 2063, 2111, 2143, 2287, 2311, 2383, 2423, 2447, 2503, 2551
Offset: 1

Views

Author

Giovanni Resta, Mar 01 2006

Keywords

Comments

Apart from the initial term (2) and few exceptional values (A116894) this sequence seems to coincide with A067658. The values of k for which the terms of this sequence are obtained are in A116893.

Examples

			gcd(1!+1,1^1+1) = 2 gives the first term;
gcd(3!+1,3^3+1) = gcd(7,28) = 7 gives the second, and so on.
		

Crossrefs

Programs

  • C
    See Links section in A116893.
  • Mathematica
    f[n_] := GCD[n! + 1, n^n + 1]; t = Array[f, 1295]; Rest@ Union@ t (* Robert G. Wilson v, Mar 09 2006 *)
  • PARI
    lista(nn) = for (n=1, nn, if ((g=gcd(n! + 1, n^n + 1)) != 1, print1(g, ", "))); \\ Michel Marcus, Jul 22 2018
    

Extensions

Entries checked by Robert G. Wilson v, Mar 09 2006
Showing 1-4 of 4 results.