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A081517
Consider the smallest number m which can be expressed as the sum of n distinct numbers coprime to m. Sequence gives triangle (read by rows) of the set of coprime numbers pertaining to m. When there is a choice, use the lexicographically earliest solution.
5
1, 1, 2, 1, 2, 4, 1, 2, 3, 5, 1, 2, 3, 4, 7, 1, 2, 3, 4, 5, 8, 1, 2, 3, 4, 5, 6, 8, 1, 2, 3, 4, 5, 6, 7, 9, 1, 2, 3, 4, 5, 6, 7, 8, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 19
OFFSET
1,3
COMMENTS
For n >= 2, it appears that m is the least prime >= n*(n+1)/2, and row n consists of
1,2,3,...,n-1 and m - n*(n-1)/2. Robert Israel, Dec 22 2024
LINKS
Robert Israel, Table of n, a(n) for n = 1..7260 (first 120 rows, flattened)
EXAMPLE
Triangle begins:
1;
1,2;
1,2,4;
1,2,3,5;
1,2,3,4,7;
1,2,3,4,5,8;
MAPLE
g:= proc(S, m, n) # lex-first sublist of sorted list S of size n with sum m, or FAIL
option remember;
local nS, i, v;
nS:= nops(S);
if nS < n or convert(S[1..n], `+`) > m or convert(S[-n .. -1], `+`) < m then return FAIL fi;
if n = 0 then if m = 0 then return [] else return FAIL fi fi;
for i from 1 to nS while S[i] <= m do
v:= procname(S[i+1..-1], m-S[i], n-1);
if v <> FAIL then return [S[i], op(v)] fi
od;
FAIL
end proc:
f:= proc(n) local m, v;
for m from 1 do
v:= g(select(t -> igcd(t, m) = 1, [$1..m]), m, n);
if v <> FAIL then return op(v) fi
od
end proc:
for n from 1 to 20 do f(n) od; # Robert Israel, Dec 22 2024
PROG
(PARI) row(n) = {my(m=n*(n-1)/2, v); for(k=m+n, oo, v=List([1]); for(i=2, k-m, if(gcd(k, i)==1, listput(v, i))); if(#v>=n, forsubset([#v, n], w, if(sum(i=1, n, v[w[i]])==k, return(vector(n, i, v[w[i]])))))); } \\ Jinyuan Wang, May 23 2020
CROSSREFS
Sequence in context: A300792 A132082 A129644 * A374577 A104778 A356184
KEYWORD
nonn,tabl
AUTHOR
Amarnath Murthy, Mar 27 2003
EXTENSIONS
More terms from R. J. Mathar, Mar 23 2007
More terms from Jinyuan Wang, May 23 2020
STATUS
approved