A075077 a(1) = 1 and then the smallest number not occurring earlier such that a(n) + a(n+1) gives a different composite number (not obtained earlier).

1, 3, 5, 4, 2, 8, 6, 9, 7, 11, 10, 12, 13, 14, 16, 17, 15, 19, 20, 18, 22, 23, 21, 25, 24, 26, 28, 27, 29, 31, 32, 30, 34, 35, 33, 37, 38, 36, 40, 41, 39, 43, 42, 44, 46, 45, 47, 48, 50, 49, 51, 53, 52, 54, 56, 55, 57, 58, 59, 60, 61, 62, 63, 65, 64, 66, 67, 68, 70, 71, 69, 73

Offset

1,2

Comments

Conjecture: for n > 6, n - 2 <= a(n) <= n + 1. - Robert Israel, Jun 01 2026

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

19 (not 18) follows 15 though 15+18 = 33 is also composite but 33 is already obtained as 16 +17.

Maple

N:= 200: R:= 1: r:= 1: Cands:= [$2..N]: Comps:= remove(isprime, [$4..2*N]): nC:= nops(Cands):
do
  found:= false;
  for i from 1 to nC do
    if r + Cands[i] > Comps[-1] then break fi;
    v:= ListTools:-BinarySearch(Comps, r+Cands[i]);
    if v > 0 then found:= true; break fi;
  od;
  if not found then break fi;
  R:= R, Cands[i]; r:= Cands[i]; Cands:= subsop(i=NULL, Cands); nC:= nC-1;
  Comps:= subsop(v=NULL, Comps);
od:
R; # Robert Israel, Jun 01 2026

Crossrefs

Cf. A075078.

Sequence in context: A378684 A381664 A381663 * A196771 A266121 A340255

Adjacent sequences: A075074 A075075 A075076 * A075078 A075079 A075080

Keyword

nonn,changed

Author

Amarnath Murthy, Sep 09 2002

Extensions

More terms from Sascha Kurz, Feb 01 2003

Status

approved