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

1,1

Links

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

Example

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

Maple

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

Crossrefs

Cf. A083521, A002383.

Sequence in context: A093431 A243765 A256148 * A336801 A162869 A079018

Adjacent sequences: A083517 A083518 A083519 * A083521 A083522 A083523

Keyword

nonn

Author

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

Extensions

More terms from David Wasserman, Nov 19 2004

Status

approved