A116891 -id:A116891 - cp's OEIS frontend

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

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

Giovanni Resta, Mar 01 2006

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

			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.

Nick Hobson, Table of n, a(n) for n = 1..10000 (first 1832 terms from Antti Karttunen)
Nick Hobson, C program.

Cf. A014566, A038507, A067658, A116891, A116892, A116894.

C
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See Links section.
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Select[Range[1500], (GCD[ #!+1, #^#+1] > 1)&]

isok(n) = gcd(n! + 1, n^n + 1) != 1; \\ Michel Marcus, Jul 22 2018

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

Giovanni Resta, Mar 01 2006

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.

			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.

Nick Hobson, Table of n, a(n) for n = 1..10000 (first 1832 terms from Antti Karttunen)

Cf. A014566, A038507, A067658, A116891, A116893, A116894.

C
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See Links section in A116893.
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f[n_] := GCD[n! + 1, n^n + 1]; t = Array[f, 1295]; Rest@ Union@ t (* Robert G. Wilson v, Mar 09 2006 *)

lista(nn) = for (n=1, nn, if ((g=gcd(n! + 1, n^n + 1)) != 1, print1(g, ", "))); \\ Michel Marcus, Jul 22 2018

Entries checked by Robert G. Wilson v, Mar 09 2006

A116894 Numbers k such that gcd(k! + 1, k^k + 1) is neither 1 nor 2k+1.

Original entry on oeis.org

1, 5427, 41255, 43755, 208161, 496175, 497135

Offset: 1

Giovanni Resta, Mar 01 2006

g(n) = gcd(n! + 1, n^n + 1) is almost always equal to 1 or to 2n+1. These are the known exceptions: g(1) = 2, g(5427) = 10453, g(41255) = 129341, g(43755) = 157519, g(208161) = 555097. - Hans Havermann, Mar 28 2006

a(8) > 1000000. - Nick Hobson, Feb 20 2024

			gcd(1! + 1, 1^1 + 1) = 2 and 2 != 2*1 + 1, so 1 belongs to the sequence.

Cf. A014566, A038507, A067658, A116891, A116892, A116893.

C
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// See Links section in A116893.
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a(5) from Hans Havermann, Mar 28 2006

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

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

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

C

Mathematica

PARI

Extensions

A116894 Numbers k such that gcd(k! + 1, k^k + 1) is neither 1 nor 2k+1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

C

Extensions