This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A230387 #30 Dec 23 2024 14:53:43
%S A230387 1,3,17,139,795,3903,28575
%N A230387 Least sum of a set of n odious numbers (A000069) such that the sum of two or more is an evil number (A001969).
%C A230387 Is this sequence finite, or is there for any n at least one admissible set of n odious numbers, i.e., such that any sum of two or more elements add up to an evil number?
%H A230387 M. F. Hasler, in reply to V. Shevelev, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-October/011785.html">Peculiar sets of evil numbers (Cf. A001969)</a>, SeqFan list, Oct 17 2013
%F A230387 Row sums of A230384.
%e A230387 For n=1 to 4, we have the sets
%e A230387 n=1: {1} with sum = 1,
%e A230387 n=2: {1, 2} with sum = 3
%e A230387 n=3: {2, 7, 8} with sum = 17,
%e A230387 n=4: {4, 19, 49, 67} with sum = 139.
%e A230387 E.g., for n=3, the numbers 2, 7 and 8 have an odd bit sum, but 2+7, 2+8, 7+8 and 2+7+8 all have an odd bit sum.
%e A230387 For n=4, we also have the admissible set {14, 31, 44, 61} which has a smaller maximal element, but a larger total sum.
%e A230387 n=5: {42, 84, 138, 174, 357} with sum = 795.
%e A230387 n=6: {168, 348, 372, 702, 906, 1407} with sum = 3903.
%e A230387 n=7: {2273, 2274, 2276, 2280, 2288, 3296, 13888} with sum = 28575.
%o A230387 (PARI) A69=select(is_A69=n->bittest(hammingweight(n),0),vector(700,n,n)); A230387(n,m=9e9)={ local(v=vector(n,i,i), ve=vector(n,i,A69[i]), t=0, s=vector(n,i,if(i>1,A230387(i-1))), ok(e)=!forstep(i=3,2^#e-1,2, is_A69( sum( j=1,#t=vecextract(e,i),t[j] )) && 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]=A69[v[j]]); ve[j]=A69[v[j]=j])/*end for*/; ve[n]=A69[v[n]++]);/*end of 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=min(sum(j=1,n,ve[j]),m); inc(n));m} /* Note: The code may find a(n) earlier but won't return it unless A69 is precomputed up to the limit a(n) - a(n-1); so e.g. 700 is enough for a(5).*/
%Y A230387 Cf. A230386, A230385.
%K A230387 nonn,base,more,hard
%O A230387 1,2
%A A230387 _M. F. Hasler_, Oct 17 2013
%E A230387 a(5)-a(6) from _Charles R Greathouse IV_, Oct 18 2013
%E A230387 a(7) from _Donovan Johnson_, Oct 27 2013