OFFSET
0,1
COMMENTS
Obviously a(n) is a lower limit for any s solution to 2*s^n = Sum_{x in S} x^n, S subset of {1, ..., s-1}.
First differences are (2, 3, 2, 3, ...) except for a duplicated 2 in positions {16, 31, 46, 61, 76, 91; 104, 119, 134, 149, 164, 179, 194, 209, 224, 239, 254, 269; 282, 297, ...}: Here the first differences are always 15 except for a 13 after the 6th, 18th, ... term.
FORMULA
a(n) >= A195168(n+1) with equality for n not in {13, 15; 26, 28, 30; 39, 41, 43, 45; 52, 54, ..., 60; 65, 67, ..., 75, 78, 80, ..., 90; 89, 91, ..., 103; 102, 104, ..., 114, 115, ...} \ {120, 122, 124, 126, 135, 137, 139, 150, 152, 165}.
a(n) <= A047218(n+2) with equality for n <= 17 and even n <= 34.
Conjecture: a(n) = round(n/log(3/2) + 3).
EXAMPLE
For n=0, 2*m^0 = 2 > Sum_{k<m} k^0 = m - 1 <=> 3 > m, so a(0) = 3.
For n=1, 2*m^1 > Sum_{k<m} k^1 = m(m-1)/2 <=> 4 > m - 1, so a(1) = 5.
MATHEMATICA
Table[Block[{m = 1, s = 0}, While[2 m^n > s, s = s + m^n; m++]; m], {n, 0, 66}] (* Michael De Vlieger, Apr 30 2020 *)
PROG
(PARI) apply( A332102(n, s)=for(m=1, oo, s<2*m^n||return(m); s+=m^n), [0..66])
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Apr 18 2020
STATUS
approved