A079932 - OEIS

%I #4 Apr 05 2014 09:58:10

%S 1,4,10,13,22,27,32,36,40,49,54,62,66,71,80,91,97,102,109,114,120,124,

%T 127,138,146,149,159,165,169,180,184,187,194,202,208,219,224,231,235,

%U 248,258,263,266,274,281,287,294,300,304,308,316,323,329,337,343,350

%N Greedy powers of (1/sqrt(2)): sum_{n=1..inf} (1/sqrt(2))^a(n) = 1.

%C The n-th greedy power of x, when 0.5 < x < 1, is the smallest integer exponent a(n) that does not cause the power series sum_{k=1..n} x^a(k) to exceed unity.

%F a(n)=sum_{k=1..n}floor(g_k) where g_1=1, g_{n+1}=log_x(x^frac(g_n) - x) (n>0) at x=(1/sqrt(2)) and frac(y) = y - floor(y).

%e a(3)=10 since (1/sqrt(2)) + (1/sqrt(2))^4 + (1/sqrt(2))^10 < 1 and (1/sqrt(2)) + (1/sqrt(2))^4 + (1/sqrt(2))^9 > 1; the power 9 makes the sum > 1, so 10 is the 3rd greedy power of (1/sqrt(2)).

%Y Cf. A076796-A076802, A077468-A077475, A079930, A079931, A079933.

%K easy,nonn

%O 1,2

%A Ulrich Schimke (ulrschimke(AT)aol.com), Jan 16 2003