A138857 Numbers such that all subsets of {a(1)^2,...,a(n)^2} have a different sum.

1, 2, 3, 4, 6, 9, 12, 18, 25, 34, 49, 70, 99, 140, 198, 280, 396, 560, 792, 1120, 1584, 2241, 3169, 4482, 6339, 8965, 12678, 17930, 25357, 35860, 50714, 71721, 101429, 143442, 202858, 286885, 405717, 573770, 811434, 1147541, 1622868, 2295082, 3245736, 4590164, 6491473, 9180329, 12982946, 18360658, 25965892, 36721317, 51931785, 73442634, 103863570, 146885269, 207727140, 293770539

Offset: 1

Author

M. F. Hasler, Apr 09 2008

Keywords

• nonn

Comments

Since the ratio of two successive terms of A138858 tends to 1:2, we have here lim a(n+1)/a(n) = sqrt(2). More precisely, one has a(n) ~ 2^(n/2+const.).

See A138858 for more comments.

Links

• Martin Fuller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A138858(n)=a(n)^2, A138856, A138000, A138001, A064934, A382381.

Programs

PARI

{s=1;p=0; for( n=1,23, until( !bitand( s, s>>(p^2) ), p++); s+=s<<(p^2); print1( p,","))}

Formula

A138857(n)=sqrt(A138858(n))

Extensions

a(24)-a(30) from Donovan Johnson, Oct 03 2009

a(31) onwards from Martin Fuller, Apr 07 2025