A102330 Triangle read by rows: n-th row consists of the lexicographically earliest set of n distinct primes whose sum is A068873(n).

2, 2, 3, 3, 5, 11, 2, 3, 5, 7, 3, 5, 7, 11, 17, 2, 3, 5, 7, 11, 13, 3, 5, 7, 11, 13, 17, 23, 2, 3, 5, 7, 11, 13, 19, 23, 3, 5, 7, 11, 13, 17, 19, 23, 29, 2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 3, 5, 7, 11, 13, 17

Offset: 1

Author

Giovanni Teofilatto, Jan 30 2005

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins:
  2
  2,3
  3,5,11
  2,3,5,7
  3,5,7,11,17
  2,3,5,7,11,13
  3,5,7,11,13,17,23
  2,3,5,7,11,13,19,23
  3,5,7,11,13,17,19,23,29
  2,3,5,7,11,13,17,19,23,31
  3,5,7,11,13,17,19,23,29,31,41
  2,3,5,7,11,13,17,19,23,29,31,37
  3,5,7,11,13,17,19,23,29,31,37,41,47
  2,3,5,7,11,13,17,19,23,29,31,37,41,43
  3,5,7,11,13,17,19,23,29,31,37,41,43,47,53
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10011 (first 141 rows flattened, first 300 terms from Jean-Francois Alcover, terms 301..2485 from Robert Israel)
• Robert Israel, Table of n, a(n) for n = 1..2485 (rows 1 to 70, flattened), replacing incorrect b-file from Jean-Francois Alcover

Crossrefs

By definition, row sums are A068873.

Programs

Maple

g:= proc(n,k,m) option remember; # lex earliest set of k distinct primes > m with sum n
   local q,v;
  if k = 1 then
    if isprime(n) and n > m then return [n] else return NULL fi
  fi;
  q:= m;
  do
    q:= nextprime(q);
    if n < k*q then return NULL fi;
    v:= procname(n-q,k-1,q);
    if v <> NULL then return [q,op(v)] fi
  od
end proc:
f:= proc(k)
local p,i,v;
p:= add(ithprime(i),i=1..k)-1;
do
  p:= nextprime(p);
  v:= g(p,k,0);
  if v <> NULL then return v fi
od
end proc:
for k from 1 to 30 do
  f(k)
od; # Robert Israel, May 12 2025

Mathematica

(* Computation verified with A068873. *)
row[n_] := Module[{s, m}, s = Select[{#, Total[#]}& /@ Subsets[ Prime[ Range[n+4]], {n}], PrimeQ[#[[2]]]&]; m = MinimalBy[s, #[[2]]&, 1]; If[s != {}, Return[m[[1, 1]]]]];
Array[row, 49] // Flatten (* Jean-François Alcover, Apr 23 2020 *)

Extensions

Edited, corrected and extended by Ray Chandler, Feb 02 2005

Edited by N. J. A. Sloane, May 07 2014