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.

3, 4, 114, 852, 1648, 1847, 2500, 22765, 54954, 59930, 47350, 971579, 2183012, 1945709, 14424271, 19139070, 19517159, 122815056, 318016298, 72732221, 575945350, 1020650071, 3009991871, 3411065961, 9193759213, 847932178, 310400972174, 221060379834, 125367239529, 426824249940

Offset: 1

Author

Joseph L. Pe, Jan 03 2002

Keywords

• nonn

Comments

Equivalently, a(n) is the least k such that prime(k+1) - prime(k) = prime(k) - prime(k-n). - Giovanni Resta, Apr 03 2017

Examples

			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.
		

Crossrefs

Cf. A000720, A089344.

Programs

Mathematica

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 *)

Formula

a(n) = A000720(A089344(n)). - Giovanni Resta, Apr 04 2017

Extensions

a(6)-a(30) from Giovanni Resta, Apr 04 2017

Definition corrected by David A. Corneth, Apr 04 2017