A232095 - OEIS

%I #15 Dec 11 2021 04:37:52

%S 0,1,2,1,3,4,5,3,3,6,4,5,4,7,7,1,5,5,5,8,7,9,5,5,6,8,10,6,9,8,10,8,6,

%T 10,12,7,10,11,6,5,7,7,8,9,5,8,5,6,8,7,10,7,11,14,8,8,6,11,7,10,7,12,

%U 10,10,12,14,7,12,9,9,11,9,12,12,12,14,10,7,11,11

%N Minimal number of factorials which add to 0+1+2+...+n; a(n) = A034968(A000217(n)).

%C 1's occur at positions n=1, n=3 and n=15 as they are such natural numbers that A000217(n) is also one of the factorial numbers (A000142), as we have A000217(1) = 1 = 1!, A000217(3) = 1+2+3 = 6 = 3! and A000217(15) = 1 + 2 + ... + 15 = 120 = 5!

%C On the other hand, a(2)=2, as A000217(2) = 1+2 = 3 = 2! + 1!. Is this the only occurrence of 2?

%C Are some numbers guaranteed to occur an infinite number of times?

%H Antti Karttunen, <a href="/A232095/b232095.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A034968(A000217(n)).

%F a(n) = A231717(A226061(n+1)). [Not a practical way to compute this sequence. Please see comments at A231717.]

%F For all n, a(n) >= A232094(n).

%o (Scheme)

%o (define (A232095 n) (A034968 (A000217 n)))

%Y Cf. A232094, A232096.

%K nonn

%O 0,3

%A _Antti Karttunen_, Nov 18 2013