A162842 a(1)=1, a(2)=2; for n > 2, a(n) is the smallest m that has not yet appeared and is not divisible by any pairwise sum of a(1)..a(n-1).

1, 2, 4, 7, 13, 19, 29, 37, 43, 49, 58, 61, 67, 73, 79, 89, 97, 103, 109, 127, 133, 139, 149, 157, 163, 169, 179, 193, 199, 211, 223, 229, 239, 247, 259, 271, 277, 283, 293, 298, 301, 307, 313, 331, 337, 343, 349, 358, 361, 367, 373, 379, 397, 409, 421, 427, 433

Offset

1,2

Comments

Strictly increasing sequence.

Links

Table of n, a(n) for n=1..57.

Example

a(1)=1, a(2)=2, a(3)=4, pairwise sums=pws={3,5,6}; smallest m that has not yet appeared and is not divisible by any of pws is m=7 hence a(4)=7; now pws={3,5,6,8,9,11}; hence a(5)=13, etc.

Mathematica

s={1, 2}; ps={3}; a=2; Do[Do[If[Mod[n, ps[[i]]]==0, Goto[ne]], {i, Length[ps]}]; a=n; ps=Union[Flatten[{ps, s+a}]]; AppendTo[s, a]; Label[ne], {n, 3, 1000}]; s

Prog

(PARI) {S=[]; for(n=1, 999, for(i=2, #S, for(j=1, i-1, n%(S[i]+S[j]) || next(3))); S=concat(S, n); print1(n", "))} \\ M. F. Hasler, Aug 30 2009

Crossrefs

Cf. A164901.

Sequence in context: A163522 A255173 A002466 * A164901 A262744 A359516

Adjacent sequences: A162839 A162840 A162841 * A162843 A162844 A162845

Keyword

nonn

Author

Zak Seidov, Jul 14 2009

Extensions

Terms corrected by M. F. Hasler, Aug 30 2009

Status

approved