cp's OEIS Frontend

A066496 a(n) = least solution k of f(k) = f(k-1) + ... + f(k-n), where f(m) = prime(m+1)-prime(m) and prime(m) denotes the m-th prime, if k exists; 0 otherwise.

%I A066496 #12 Apr 05 2017 04:30:25
%S A066496 3,4,114,852,1648,1847,2500,22765,54954,59930,47350,971579,2183012,
%T A066496 1945709,14424271,19139070,19517159,122815056,318016298,72732221,
%U A066496 575945350,1020650071,3009991871,3411065961,9193759213,847932178,310400972174,221060379834,125367239529,426824249940
%N A066496 a(n) = least solution k of f(k) = f(k-1) + ... + f(k-n), where f(m) = prime(m+1)-prime(m) and prime(m) denotes the m-th prime, if k exists; 0 otherwise.
%C A066496 Equivalently, a(n) is the least k such that prime(k+1) - prime(k) = prime(k) - prime(k-n). - _Giovanni Resta_, Apr 03 2017
%F A066496 a(n) = A000720(A089344(n)). - _Giovanni Resta_, Apr 04 2017
%e A066496 3 is the smallest solution of f(k) = f(k-1); so a(1) = 3. 4 is the smallest solution of f(k) = f(k-1)+f(k-2); so a(2) = 4. 114 is the smallest solution of f(k) = f(k-1)+f(k-2)+f(k-3); so a(3) = 114.
%t A066496 a[n_] := Block[{k=n+1}, While[2 Prime[k] != Prime[k + 1] + Prime[k - n], k++]; k]; Array[a, 8] (* _Giovanni Resta_, Apr 03 2017 *)
%Y A066496 Cf. A000720, A089344.
%K A066496 nonn
%O A066496 1,1
%A A066496 _Joseph L. Pe_, Jan 03 2002
%E A066496 a(6)-a(30) from _Giovanni Resta_, Apr 04 2017
%E A066496 Definition corrected by _David A. Corneth_, Apr 04 2017