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
A067364 a(n)=p-n!^4, where p is the smallest prime > n!^4+1.
2, 3, 5, 5, 7, 29, 19, 29, 181, 19, 31, 173, 79, 43, 379, 61, 101, 127, 101, 83, 37, 29, 271, 233, 109, 233, 293, 1039, 137, 241, 173, 197, 613, 1933, 277, 71, 503, 449, 1667, 53, 67, 163, 179, 211, 53, 613, 1171, 1069, 359, 199, 839, 433, 1523, 463, 677
Offset: 1
Keywords
Comments
The first 102 terms are primes. Are all terms prime? For n!^i, with 0
The first 1865 terms are primes. - Dana Jacobsen, May 13 2015
Links
- Dana Jacobsen, Table of n, a(n) for n = 1..1865
- Cyril Banderier, Fortunate Numbers
Programs
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Mathematica
a[n_] := For[i=2, True, i++, If[PrimeQ[n!^4+i], Return[i]]]
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MuPAD
for n from 1 to 50 do f := n!^4:a := nextprime(f+2)-f:print(a) end_for
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PARI
for(n=1, 500, f=n!^4; 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)**4; 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
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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