A005242 Lexicographically earliest sequence of distinct positive integers such that sums of two or three consecutive earlier terms are excluded. (Formerly M0971)

1, 2, 4, 5, 8, 10, 12, 14, 15, 16, 19, 20, 21, 24, 25, 27, 28, 32, 33, 34, 37, 38, 40, 42, 43, 44, 46, 47, 48, 51, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 68, 69, 72, 73, 74, 77, 79, 81, 83, 84, 86, 88, 89, 91, 92, 94, 96, 97, 98, 100

Offset

1,2

Comments

Presumably this is the lexicographically earliest sequence of distinct positive numbers with the property that sums of two or three consecutive earlier terms are excluded. - N. J. A. Sloane, Jan 07 2021

References

R. K. Guy, Unsolved Problems in Number Theory, E30.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Prime Number of Measurement.

Prog

(Haskell)
import Data.List ((\\))
a005242 n = a005242_list !! (n-1)
a005242_list = f [1..] 0 0 where
   f (x:xs) y z = x : f (xs \\ [x + y, x + y + z]) x y
-- Reinhard Zumkeller, May 23 2013
(Python)
import itertools
def a005242_gen():
    terms, forbidden = [1, 2], {3}
    yield from terms
    while True:
        for c in itertools.count(terms[-1] + 1):
            if c not in forbidden:
                break
        yield c
        terms.append(c)
        forbidden.add(terms[-1] + terms[-2])
        forbidden.add(terms[-1] + terms[-2] + terms[-3])
a005242_list = list(itertools.islice(a005242_gen(), 30))
# Adam Reichert, May 31 2026

Crossrefs

Cf. A002048, A033627.

Sequence in context: A188972 A047612 A123886 * A323976 A188975 A115392

Adjacent sequences: A005239 A005240 A005241 * A005243 A005244 A005245

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Jud McCranie, Feb 15 1997

Name clarified from comment by N. J. A. Sloane, Jan 07 2021. - Adam Reichert, May 31 2026

Status

approved