A092464 -id:A092464 - cp's OEIS frontend

A094550 Numbers n such that there are integers a < b with a+(a+1)+...+(n-1) = (n+1)+(n+2)+...+b.

4, 6, 9, 11, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 34, 35, 36, 38, 39, 40, 41, 43, 44, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 59, 61, 64, 66, 68, 69, 70, 71, 72, 74, 76, 77, 79, 81, 82, 83, 84, 86, 87, 89, 91, 93, 94, 95, 96, 97, 98, 99, 100, 101, 104

Offset: 1

T. D. Noe, May 10 2004

Liljestrom shows that n is in this sequence if and only if 4n^2+1 is composite.
Complement of A001912.
From Hermann Stamm-Wilbrandt, Sep 16 2014: (Start)
For n > 1, A047209 is a subset of this sequence [ 4*n^2+1 is divisible by 5 if n is (1 or 4) mod 5].
A092464 is a subset of this sequence [4*n^2+1 is divisible by 13 if n is (4 or 9) mod 13].
The above are for divisibility by 5, 13; notation (1,4,5), (4,9,13). Divisibility by p for a and p-a; notation (a,p-a,p). These are the next tuples: (2,15,17), (6,23,29), (3,34,37), (16,25,41), ... . The corresponding sequences are a subset of this sequence [ 2,15,19,32,36,49,... for (2,15,17) ]. These sequences have no entries in the OEIS yet. For any prime of the form 4*k+1 there is exactly one of these tuples/sequences [solution to 4*a^2+1=0 (mod p)].
For n>1, A000290 (squares) is a subset of this sequence (4,9,16,25,...) [ 4*(m^2)^2+1 is divisible by  m^2+(m+1)^2, tuple (m^2, (m+1)^2, m^2+(m+1)^2) ].
(End)

			6 is in this sequence because 1+2+3+4+5 = 7+8.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
R. J. Liljestrom and Richard Zucker, Numerical Fulcrums (PowerPoint Format)

Cf. A094551, A094552, A094553.

Cf. A001912.

[n: n in [1..100] |not IsPrime(4*n^2 + 1)]; // Vincenzo Librandi, Sep 27 2012

lst={}; Do[i1=n-1; i2=n+1; s1=i1; s2=i2; While[i1>1 && s1!=s2, If[s1T. D. Noe, Nov 12 2010 *)

A127547 a(n) = 13*n + 4.

Original entry on oeis.org

4, 17, 30, 43, 56, 69, 82, 95, 108, 121, 134, 147, 160, 173, 186, 199, 212, 225, 238, 251, 264, 277, 290, 303, 316, 329, 342, 355, 368, 381, 394, 407, 420, 433, 446, 459, 472, 485, 498, 511, 524, 537, 550, 563, 576, 589, 602, 615, 628, 641, 654, 667, 680, 693, 706, 719

Offset: 0

Robert H Barbour, Apr 01 2007

Superhighway created by 'LQTL Ant' L90R90L45R45 from iteration 4 where the Ant moves in a 'Moore neighborhood' (nine cells), the L indicates a left turn, the R a right turn, and the numerical value is the size of the turn (in degrees) at each iteration.

Ant Farm algorithm available from Robert H Barbour.

P. Sakar, "A Brief History of Cellular Automata," ACM Computing Surveys, vol. 32, pp. 80-107, 2000.

G. C. Greubel, Table of n, a(n) for n = 0..5000
C. Langton, Studying Artificial Life with Cellular Automata, Physica D: Nonlinear Phenomena, vol. 22, pp. 120-149, 1986.
James Propp, Further Ant-ics, Mathematical Intelligencer, 16 pp. 37-42, 1994.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

A subsequence of A092464.
Cf. A126979, A126980.
Sequences of the form 13*n+q: A008595 (q=0), A190991 (q=1), A153080 (q=2), this sequence (q=4), A154609 (q=5), A186113 (q=6), A269044 (q=7), A269100 (q=11).

[13*n+4: n in [0..60]]; // G. C. Greubel, May 31 2024

Range[4,1000,13] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)

[13*n+4 for n in range(61)] # G. C. Greubel, May 31 2024

From Elmo R. Oliveira, Mar 21 2024: (Start)
G.f.: (4+9*x)/(1-x)^2.
E.g.f.: (4 + 13*x)*exp(x).
a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)

Edited by N. J. A. Sloane, May 10 2007

cp's OEIS Frontend

A094550 Numbers n such that there are integers a < b with a+(a+1)+...+(n-1) = (n+1)+(n+2)+...+b.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica