A083521 -id:A083521 - cp's OEIS frontend

A083520 Primes p such that p-1 is a product of two or more consecutive integers. Or (p-1) is a permutation of m items chosen from n, for some m and n. p-1 = k*(k+1)(k+2)...(k+r) for some k and r, r>0.

3, 7, 13, 31, 43, 61, 73, 157, 211, 241, 307, 337, 421, 463, 601, 757, 991, 1123, 1321, 1483, 1723, 2521, 2551, 2731, 2971, 3307, 3361, 3541, 3907, 4423, 4831, 5113, 5701, 6007, 6163, 6481, 6841, 8011, 8191, 9241, 9901, 10303, 10627, 11131, 12211, 12433

Offset: 1

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 05 2003

nonn

			61 is in this sequence as 60 = 3*4*5. 73 is in this sequence as 72 = 8*9.

R. J. Mathar, Table of n, a(n) for n = 1..131

Cf. A083521, A002383.

isA083520 := proc(p)
    local k,r,i,po;
    for k from 1 to floor(sqrt(p)) do
        for r from 1 do
            po := product(k+i,i=0..r) ;
            if po  = p-1 then
                return true;
            elif po > p-1 then
                break;
            end if;
        end do:
    end do:
    false ;
end proc:
n := 1 :
for c from 1 do
    p := ithprime(c) ;
    if isA083520(p) then
        printf("%d %d\n",n,p) ;
        n := n+1 ;
    end if;
end do: # R. J. Mathar, Aug 23 2014

More terms from David Wasserman, Nov 19 2004

A083522 Smallest k such that k(k+1)(k+2)...(k+n-1) + 1 is prime, or 0 if no such number exists.

Original entry on oeis.org

1, 1, 1, 0, 3, 3, 4, 4, 6, 2, 1, 10, 5, 3, 9, 6, 6, 4, 5, 8, 6, 7, 19, 25, 11, 2, 1, 3, 9, 23, 7, 7, 39, 5, 7, 2, 1, 5, 78, 2, 1, 15, 19, 12, 17, 6, 3, 14, 8, 21, 23, 17, 14, 40, 16, 6, 8, 13, 15, 5, 15, 82, 46, 51, 39, 43, 6, 11, 61, 57, 16, 2, 1, 26, 54, 2, 1, 13, 4, 62, 31, 69, 27, 155, 21

Offset: 1

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 05 2003

nonn

The product of four consecutive integers + 1 is always composite (a square), so a(4) = 0. Are there any more zeros in the sequence?

Since rather large numbers (up to 193 digits) are encountered in the computation, the Pocklington-Lehmer "P-1" primality test is used, as implemented in PARI 2.1.3.

			1*2*3*4*5 + 1 = 121 = 11*11 and 2*3*4*5*6 + 1 = 721 = 7*103 are composite, but 3*4*5*6*7 + 1 = 2521 is prime, so a(5) = 3.

Cf. A083520, A083521.

m=1000; for(n=1,85,b=0; k=1; while(b<1&&k

Edited and extended by Klaus Brockhaus and Don Reble, May 06 2003

cp's OEIS Frontend

A083520 Primes p such that p-1 is a product of two or more consecutive integers. Or (p-1) is a permutation of m items chosen from n, for some m and n. p-1 = k*(k+1)(k+2)...(k+r) for some k and r, r>0.

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A083522 Smallest k such that k(k+1)(k+2)...(k+n-1) + 1 is prime, or 0 if no such number exists.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Extensions

cp's OEIS Frontend

A083520 Primes p such that p-1 is a product of two or more consecutive integers. Or (p-1) is a permutation of m items chosen from n, for some m and n. p-1 = k*(k+1)(k+2)...(k+r) for some k and r, r>0.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Extensions

A083522 Smallest k such that k*(k+1)*(k+2)*...*(k+n-1) + 1 is prime, or 0 if no such number exists.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Extensions

A083522 Smallest k such that k(k+1)(k+2)...(k+n-1) + 1 is prime, or 0 if no such number exists.