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 program

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:
    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
print(terms)
# David Consiglio, Jr., Apr 18 2018
(Python)
from collections import Counter
def A303600_list(num_terms):
    terms = [2, 3]
    sum_counts = Counter([4, 5, 6])
    next_term = 3
    for n in range(2, num_terms):
        next_term += 1
        while sum_counts[next_term] != 1: next_term += 1
        terms.append(next_term)
        for term in terms: sum_counts[term + next_term] += 1
    return terms
print(A303600_list(59))
# David Radcliffe, Jun 19 2025

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