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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
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Apr 26 2018
EXTENSIONS
More terms from David Consiglio, Jr., Apr 26 2018
STATUS
approved