A138001 -id:A138001 - cp's OEIS frontend

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

M. F. Hasler, Apr 09 2008

nonn

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.

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

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

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

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

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

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

A138856 Numbers such that all subsets of {prime(a(1)), ..., prime(a(n))} have a different sum.

Original entry on oeis.org

1, 2, 4, 5, 10, 16, 28, 47, 83, 147, 267, 481, 882, 1621, 2997, 5578, 10428, 19560, 36849, 69649, 131983, 250841, 477992, 912662, 1746404, 3347928, 6429526, 12366247, 23820901, 45947255, 88742186, 171594310, 332169919, 643674781, 1248523100, 2423948034

Offset: 1

M. F. Hasler, Apr 10 2008

nonn

See A138000, A138857 and A138858.

Cf. A064934, A138000, A138001, A138857, A138858.

{s=1;p=0; for( n=1,20, until( !bitand( s, s>>prime(p++) ),); s+=s<

a(n) = primepi(A138000(n)).

a(22)-a(30) from Donovan Johnson, Oct 03 2009

a(31)-a(36) from Amiram Eldar, Sep 06 2024

cp's OEIS Frontend

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

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