A075122 -id:A075122 - cp's OEIS frontend

A011185 A B_2 sequence: a(n) = least value such that sequence increases and pairwise sums of distinct elements are all distinct.

1, 2, 3, 5, 8, 13, 21, 30, 39, 53, 74, 95, 128, 152, 182, 212, 258, 316, 374, 413, 476, 531, 546, 608, 717, 798, 862, 965, 1060, 1161, 1307, 1386, 1435, 1556, 1722, 1834, 1934, 2058, 2261, 2497, 2699, 2874, 3061, 3197, 3332, 3629, 3712, 3868, 4140, 4447, 4640

Offset: 1

Dan Hoey

nonn

a(n) = least positive integer > a(n-1) and not equal to a(i)+a(j)-a(k) for distinct i and j with 1 <= i,j,k <= n-1. [Comment corrected by Jean-Paul Delahaye, Oct 02 2020.]

Klaus Brockhaus and Dan Hoey, Table of n, a(n) for n = 1..2839
Index entries for B_2 sequences.

Cf. A010672.
Cf. A033627, A003278, A026471, A066720, A075122, A075123, A133097.
Cf. A036241, A349777.

from itertools import islice
def agen(): # generator of terms
    aset, sset, k = set(), set(), 0
    while True:
        k += 1
        while any(k+an in sset for an in aset): k += 1
        yield k; sset.update(k+an for an in aset); aset.add(k)
print(list(islice(agen(), 51))) # Michael S. Branicky, Feb 05 2023

a(n) = A010672(n-1)+1.

A026471 a(n) = least positive integer > a(n-1) and not of the form a(i) + a(j) + a(k) for 1 <= i < j < k <= n.

Original entry on oeis.org

1, 2, 3, 4, 5, 13, 14, 15, 25, 26, 27, 37, 38, 48, 49, 50, 60, 61, 71, 72, 73, 83, 84, 94, 95, 96, 106, 107, 117, 118, 119, 129, 130, 140, 141, 142, 152, 153, 163, 164, 165, 175, 176, 186, 187, 188, 198, 199, 209, 210, 211, 221, 222, 232, 233, 234, 244, 245, 255

Offset: 1

Clark Kimberling

Wieb Bosma, Rene Bruin, Robbert Fokkink, Jonathan Grube, Anniek Reuijl, and Thian Tromp, Using Walnut to solve problems from the OEIS, arXiv:2503.04122 [math.NT], 2025.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Cf. A003278, A033627, A075122, A075123.

{1, 5, 13} union {n congruent 2, 3, 4, 14, 15 mod 23}, proved by Matthew Akeran. - Ralf Stephan, Nov 15 2004

G.f.: (9*x^11-7*x^10+9*x^8+7*x^5+x^4+x^3+x^2+x+1)*x/(x^6-x^5-x+1). - Alois P. Heinz, Aug 06 2018

Edited by Floor van Lamoen, Sep 02 2002

A075123 a(n) is the least positive integer > a(n-1) and a(n) is not 2*a(i)+a(j) for 1<=i

Original entry on oeis.org

1, 2, 3, 6, 9, 14, 17, 22, 25, 30, 33, 38, 41, 46, 49, 54, 57, 62, 65, 70, 73, 78, 81, 86, 89, 94, 97, 102, 105, 110, 113, 118, 121, 126, 129, 134, 137, 142, 145, 150, 153, 158, 161, 166, 169, 174, 177, 182, 185, 190, 193, 198, 201, 206, 209, 214, 217, 222, 225, 230

Offset: 1

Floor van Lamoen, Sep 02 2002

a(n) = A047452(n-2) for n > 3 because of first formula. - Georg Fischer, Oct 19 2018

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A003278, A026471, A033627, A047452, A075122.

Join[{1,2,3},Table[4n-10-Mod[n,2],{n,4,60}]] (* or *)
LinearRecurrence[ {1,1,-1},{1,2,3,6,9,14},60] (* Harvey P. Dale, Oct 28 2012 *)

def A075123(n): return (n-2<<2)-2-(n&1) if n>3 else n # Chai Wah Wu, Mar 30 2024

a(n) = 4n - 10 - (n mod 2), for n>3. - Ralf Stephan, Nov 16 2004
a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3. - Harvey P. Dale, Oct 28 2012
G.f.: x*(1+x+2*x^3+2*x^4+2*x^5)/((1+x)*(1-x)^2). - Georg Fischer, May 15 2019

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A011185 A B_2 sequence: a(n) = least value such that sequence increases and pairwise sums of distinct elements are all distinct.

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A026471 a(n) = least positive integer > a(n-1) and not of the form a(i) + a(j) + a(k) for 1 <= i < j < k <= n.

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A075123 a(n) is the least positive integer > a(n-1) and a(n) is not 2*a(i)+a(j) for 1<=i

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