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A300334 Primes of a056240-type 2. 3

%I #30 Mar 10 2018 14:44:21

%S 211,541,631,673,1693,1801,2879,3181,3271,3299,3343,3571,3943,4177,

%T 4441,4561,4751,4783,4813,4861,5147,5381,5431,5501,5779,6029,6197,

%U 6421,6469,6521,6599,6637,6883,7103,7321,7369,7477,7573,7603,7789,7901,7963,8419,8443,8641,8923,9091,9587,9643,9733,9781,9871,10513

%N Primes of a056240-type 2.

%C Prime(r) has a056240-type k if A295185(prime(r))=prime(r-k)*A056240(prime(r)-prime(r-k)).

%C This sequence lists primes having a056240-type k=2, each having form ~2(g1,g2) where g1 is the first gap below prime(r), and g2 is the second (notation explained in A295185). The majority of primes appear to be of a056240-type 1.

%e 211 is included because the smallest composite number whose sum of prime factors (with repetition)=211 is 6501=197*33, a multiple of the second prime below 211, not the first. 211~2(12,2) is the smallest prime to have this property. Likewise 541~2(18,2), 1693~2(24,2), 2879~2(18,4), etc.

%Y Cf. A056240, A295185, A299110, A293652, A299912, A300359.

%K nonn

%O 1,1

%A _David James Sycamore_, Mar 03 2018

%E Edited by _N. J. A. Sloane_, Mar 10 2018

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