OFFSET
1,2
COMMENTS
Is this sequence finite, or is there for any n at least one admissible set of n evil numbers, i.e., such that any sum of two or more elements add up to an odious number?
By definition, this is a subsequence of the odious numbers A000069.
LINKS
M. F. Hasler, in reply to V. Shevelev, Peculiar sets of evil numbers (Cf. A001969), SeqFan list, Oct 17 2013
EXAMPLE
The table A230385 reads
n=1: {0} with sum = 0,
n=2: {3, 5} with sum = 8,
n=3: {5, 9, 17} or {9, 10, 12} with sum = 31,
n=4: {5, 9, 17, 33} with sum = 64,
n=5: {33, 34, 36, 40, 48} with sum = 191,
n=6: {257, 264, 278, 288, 326, 384} with sum = 1797.
For example, for n=4, all 11 numbers 5+9=14, 5+17=22, 5+33=38, 9+17=26, 9+33=42, 17+33=50, 5+9+17=31, 5+9+33=47, 5+17+33=55, 9+17+33=59, 5+9+17+33=64 are odious.
n=7: {801, 802, 804, 808, 816, 4896, 9536} with sum = 18463.
PROG
(PARI) (is_A69=n->bittest(hammingweight(n), 0)); A1969=select(n->!is_A69(n), vector(1600, n, n)) /* no 0 here! */; A230386(n, m=9e9)={ local(v=vector(n, i, i), ve=vector(n, i, A1969[i]), t=0, s=vector(n, i, if(i>1, A230386(i-1))), S(v)=sum(j=1, #v, v[j]), ok(e)=!forstep(i=3, 2^#e-1, 2, is_A69( S( vecextract( e, i )))||return), inc(i)=for(j=1, n-i, v[j]=j); for(j=n-i+1, n-1, v[j]++<v[j+1] && return(ve[j]=A1969[v[j]]); ve[j]=A1969[v[j]=j])/*end for*/; ve[n]=A1969[v[n]++])/*end local()*/; while( s[n]+ve[n]<m, for(i=2, n, s[n-i+1]+sum(j=n-i+1, n, ve[j]) < m && ok(vecextract(ve, 2^n-2^(n-i))) && next; inc(i); next(2)); m>S(ve) && /*print*/([m=S(ve), ve]); inc(n)); m} /* This code is very fast up to n=5 and much too slow for n>5. */
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Vladimir Shevelev and M. F. Hasler, Oct 17 2013
EXTENSIONS
a(6) added by M. F. Hasler, Oct 18 2013
a(7) from Donovan Johnson, Oct 27 2013
STATUS
approved