A285716 - OEIS

%I #21 Aug 07 2023 11:35:57

%S 0,0,0,0,1,0,0,1,0,0,1,0,1,2,0,0,1,1,0,1,0,0,2,0,1,1,0,1,1,0,0,2,1,0,

%T 1,0,0,2,1,0,3,0,1,1,0,1,1,1,0,2,0,0,2,0,0,1,0,1,2,1,1,1,2,0,1,0,1,3,

%U 0,0,1,1,1,2,0,0,2,1,0,1,1,0,2,0,1,2,0,2,1,0,0,1,1,1,3,0,0,2,0,0,1,1,1,2,1,0,1,1,1,1,1,0,3,0,0,2,0,1,1,0

%N a(n) = A080791(A245611(n)).

%H Antti Karttunen, <a href="/A285716/b285716.txt">Table of n, a(n) for n = 1..8192</a>

%F a(1) = 0, a(2) = 1, for n > 2, a(n) = a(A285712(n)) + [n == 2 mod 3]. (Where [] is Iverson bracket, giving here 1 only if n is of the form 3k+2, and 0 otherwise.)

%F a(n) = A080791(A245611(n)).

%F For all n >= 2,  a(n) = A091304(n)-1 = A000120(A244153(n))-1. - _Antti Karttunen_, May 31 2017

%t a[n_] := PrimeOmega[2*n - 1] - 1; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jul 23 2023 *)

%o (Scheme)

%o ;; First implementation uses memoization-macro definec:

%o (definec (A285716 n) (if (<= n 2) 0 (+ (if (= 2 (modulo n 3)) 1 0) (A285716 (A285712 n)))))

%o (define (A285716 n) (A080791 (A245611 n)))

%Y One less than A091304 after the initial term.

%Y Cf. A000120, A080791, A244153, A245611, A278223, A285712, A285714, A285715.

%Y Cf. A006254 (gives the positions of zeros after initial a(1)=0.)

%K nonn

%O 1,14

%A _Antti Karttunen_, Apr 25 2017