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Smallest prime p such that p mod prime(k+1) = prime(k) for exactly n distinct k.
1

%I #5 Mar 30 2012 18:51:01

%S 2,5,23,47,283,557,5147,2273,12899,103703,146417,3369869,5037233,

%T 71067323,6484133

%N Smallest prime p such that p mod prime(k+1) = prime(k) for exactly n distinct k.

%C A156311(A049084(a(n)))=n and A156311(m)<n for m < A049084(a(n)).

%C a(15) > 10^8. [From _Donovan Johnson_, Jul 02 2010]

%e a(9) = 103703 = A000040(9910), A156311(9910) = 9:

%e 1: 2 + 3*34567 = prime(1) + prime(2)*34567 = 103703,

%e 2: 3 + 5*20740 = prime(2) + prime(3)*20740 = 103703,

%e 3: 5 + 7*14814 = prime(3) + prime(4)*14814 = 103703,

%e 4: 19 + 23*4508 = prime(8) + prime(9)*4508 = 103703,

%e 5: 131 + 137*756 = prime(32) + prime(33)*756 = 103703,

%e 6: 163 + 167*620 = prime(38) + prime(39)*620 = 103703,

%e 7: 181 + 191*542 = prime(42) + prime(43)*542 = 103703,

%e 8: 751 + 757*136 = prime(133) + prime(134)*136 = 103703,

%e 9: 20731 + 20743*4 = prime(2334) + prime(2335)*4 = 103703.

%Y A156312.

%K more,nonn

%O 0,1

%A _Reinhard Zumkeller_, Feb 07 2009

%E a(10)-a(14) from _Donovan Johnson_, Jul 02 2010