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a(n) is the smallest number m such that m-k is product of k+1 primes for k=0,1,2,...,n.
6

%I #29 Jun 09 2019 21:16:34

%S 2,5,47,107,71999,392279,305778479,24405534719,899133243623

%N a(n) is the smallest number m such that m-k is product of k+1 primes for k=0,1,2,...,n.

%C Each term of this sequence is prime.

%e a(5)=392279 because:

%e 392279 is prime;

%e 392279-1 = 2*196139;

%e 392279-2 = 3*229*571;

%e 392279-3 = 2*2*281*349;

%e 392279-4 = 5*5*13*17*71;

%e 392279-5 = 2*3*3*19*31*37;

%e 392279 is the smallest number m such that m-k is product of k+1 primes for k=0,1,2,3,4 & 5.

%t Table[m = 1; While[Table[Plus @@ Last /@ FactorInteger[Prime[m] - k], {k, 0, n}] != Range[1, n + 1], m++]; Prime[m], {n, 0, 5}] (* _Robert Price_, Jun 09 2019 *)

%Y Cf. A072664, A072875, A086560.

%K nonn,more

%O 0,1

%A _Farideh Firoozbakht_, Apr 14 2004

%E a(6) corrected by _Mike Oakes_, Jun 20 2012

%E a(7) from _Zak Seidov_, Apr 23 2017

%E a(8) from _Giovanni Resta_, Apr 27 2017