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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.

%I A083520 #9 Aug 23 2014 15:07:33
%S A083520 3,7,13,31,43,61,73,157,211,241,307,337,421,463,601,757,991,1123,1321,
%T A083520 1483,1723,2521,2551,2731,2971,3307,3361,3541,3907,4423,4831,5113,
%U A083520 5701,6007,6163,6481,6841,8011,8191,9241,9901,10303,10627,11131,12211,12433
%N 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.
%H A083520 R. J. Mathar, <a href="/A083520/b083520.txt">Table of n, a(n) for n = 1..131</a>
%e A083520 61 is in this sequence as 60 = 3*4*5. 73 is in this sequence as 72 = 8*9.
%p A083520 isA083520 := proc(p)
%p A083520     local k,r,i,po;
%p A083520     for k from 1 to floor(sqrt(p)) do
%p A083520         for r from 1 do
%p A083520             po := product(k+i,i=0..r) ;
%p A083520             if po  = p-1 then
%p A083520                 return true;
%p A083520             elif po > p-1 then
%p A083520                 break;
%p A083520             end if;
%p A083520         end do:
%p A083520     end do:
%p A083520     false ;
%p A083520 end proc:
%p A083520 n := 1 :
%p A083520 for c from 1 do
%p A083520     p := ithprime(c) ;
%p A083520     if isA083520(p) then
%p A083520         printf("%d %d\n",n,p) ;
%p A083520         n := n+1 ;
%p A083520     end if;
%p A083520 end do: # _R. J. Mathar_, Aug 23 2014
%Y A083520 Cf. A083521, A002383.
%K A083520 nonn
%O A083520 1,1
%A A083520 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 05 2003
%E A083520 More terms from _David Wasserman_, Nov 19 2004