A067362 a(n) = p - n!^2, where p is the smallest prime > n!^2+1.
2, 3, 5, 11, 7, 11, 11, 13, 23, 17, 13, 59, 23, 31, 23, 41, 59, 67, 29, 31, 103, 389, 59, 107, 47, 127, 67, 181, 101, 97, 409, 37, 61, 43, 61, 47, 263, 109, 53, 199, 167, 337, 47, 131, 127, 73, 181, 257, 191, 101, 83, 79, 181, 167, 229, 859, 421, 433, 107, 971
Offset: 1
Keywords
A067363 a(n)=p-n!^3, where p is the smallest prime > n!^3+1.
2, 3, 7, 5, 17, 11, 17, 23, 23, 103, 59, 17, 29, 79, 59, 23, 347, 307, 53, 227, 131, 83, 67, 223, 29, 59, 197, 83, 181, 293, 71, 71, 139, 43, 67, 103, 431, 743, 1279, 197, 419, 127, 271, 73, 229, 503, 211, 181, 1597, 151, 151, 197, 1013, 179, 587, 71, 137, 547
Offset: 1
Keywords
Comments
The first 118 terms are primes. Are all terms prime? For n!^i, with 0
The first 2278 terms are primes. - Dana Jacobsen, May 13 2015
Links
- Dana Jacobsen, Table of n, a(n) for n = 1..2278
- Cyril Banderier, Fortunate Numbers
Programs
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Mathematica
a[n_] := For[i=2, True, i++, If[PrimeQ[n!^3+i], Return[i]]] spn[n_]:=Module[{c=(n!)^3},NextPrime[c+1]-c]; Array[spn,60] (* Harvey P. Dale, May 25 2023 *) -
MuPAD
for n from 1 to 50 do f := n!^3:a := nextprime(f+2)-f:print(a) end_for
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PARI
for(n=1, 100, f=n!^3; print1(nextprime(f+2)-f,", ")) \\ Dana Jacobsen, May 13 2015
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Perl
use ntheory ":all"; use Math::GMP qw/:constant/; for my $n (1..500) { my $f=factorial($n)**3; say "$n ", next_prime($f+1)-$f; } # Dana Jacobsen, May 13 2015
Extensions
Edited by Dean Hickerson, Mar 02 2002
A067365 a(n) = p-n!^5, where p is the smallest prime > n!^5+1.
2, 5, 13, 13, 7, 7, 11, 71, 23, 19, 197, 17, 101, 53, 17, 47, 73, 97, 53, 433, 251, 251, 47, 263, 281, 353, 53, 61, 179, 41, 53, 401, 449, 79, 89, 1283, 367, 2011, 139, 227, 1597, 1657, 1123, 397, 131, 727, 137, 167, 89, 379, 421, 653, 223, 373, 2221, 1447
Offset: 1
Keywords
Comments
The first 60 terms are primes. Are all terms prime? For n!^i, with 0
The first 1592 terms are primes. - Dana Jacobsen, May 13 2015
Links
- Dana Jacobsen, Table of n, a(n) for n = 1..1592
- Cyril Banderier, Fortunate Numbers
Programs
-
Mathematica
a[n_] := For[i=2, True, i++, If[PrimeQ[n!^5+i], Return[i]]] spf[n_]:=Module[{c=(n!)^5},NextPrime[c+1]-c]; Array[spf,60] (* Harvey P. Dale, Feb 24 2015 *) -
MuPAD
for n from 1 to 50 do f := n!^5:a := nextprime(f+2)-f:print(a) end_for
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PARI
for(n=1, 100, f=n!^5; print1(nextprime(f+2)-f, ", ")) \\ Dana Jacobsen, May 13 2015
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Perl
use ntheory ":all"; use Math::GMP qw/:constant/; for my $n (1..500) { my $f=factorial($n)**5; say "$n ", next_prime($f+1)-$f; } # Dana Jacobsen, May 13 2015
Extensions
Edited by Dean Hickerson, Mar 02 2002
Comments
Links
Crossrefs
Programs
Mathematica
a[n_] := For[i=2, True, i++, If[PrimeQ[n!^2+i], Return[i]]] Table[p = NextPrime[(x = (n!)^2) + 1]; p - x, {n, 60}] (* Jayanta Basu, Aug 10 2013 *)MuPAD
PARI
Perl
use ntheory ":all"; use Math::GMP qw/:constant/; for my $n (1..500) { my $f=factorial($n)**2; say "$n ",next_prime($f+1)-$f; } # Dana Jacobsen, May 10 2015Extensions