A303600 a(1)=2 and a(2)=3, then a(n+1) is the smallest integer larger than a(n) that can be written as the sum of two (not necessarily distinct) earlier terms in exactly one way.

2, 3, 4, 5, 9, 10, 11, 16, 22, 24, 28, 29, 30, 37, 42, 50, 55, 56, 70, 73, 76, 82, 89, 95, 101, 102, 115, 128, 133, 135, 136, 141, 142, 153, 160, 161, 168, 174, 181, 195, 199, 200, 214, 221, 227, 233, 247, 252, 265, 266, 267, 273, 280, 285, 286, 325, 331, 332, 338

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (Terms 1..100 from David Consiglio, Jr.)

David A. Corneth, PARI-prog

Borys Kuca, Structures in Additive Sequences, arXiv:1804.09594 [math.NT], 2018. See V(2,3).

Mathematica

Nest[Append[#, Function[{m, s}, First@ SelectFirst[Tally[s], And[First@ # > m, Last@ # < 3] &]] @@ {Max@ #, Sort[Total /@ Tuples[#, {2}]]}] &, {2, 3}, 57] (* Michael De Vlieger, Apr 27 2018 *)

Prog

(PARI) \\ See PARI link \\ David A. Corneth, Apr 27 2018
(Python)
terms = [2, 3]
while len(terms) < 100:
    print(len(terms))
    options = []
    for x in range(len(terms)):
        for y in range(x, len(terms)):
            options.append(terms[x]+terms[y])
    for y in sorted(options):
        if options.count(y) == 1 and y > max(terms):
            terms.append(y)
            break
for x in range(len(terms)):
    print(str(x+1)+" "+terms[x])
# David Consiglio, Jr., Apr 18 2018

Crossrefs

Cf. A004280 (with first terms 1 and 2).

Sequence in context: A118732 A118872 A046029 * A194410 A361125 A081869

Adjacent sequences: A303597 A303598 A303599 * A303601 A303602 A303603

Keyword

nonn

Author

Michel Marcus, Apr 26 2018

Extensions

More terms from David Consiglio, Jr., Apr 26 2018

Status

approved