A004793 a(1)=1, a(2)=3; a(n) is least k such that no three terms of a(1), a(2), ..., a(n-1), k form an arithmetic progression.

1, 3, 4, 6, 10, 12, 13, 15, 28, 30, 31, 33, 37, 39, 40, 42, 82, 84, 85, 87, 91, 93, 94, 96, 109, 111, 112, 114, 118, 120, 121, 123, 244, 246, 247, 249, 253, 255, 256, 258, 271, 273, 274, 276, 280, 282, 283, 285, 325, 327, 328, 330, 334, 336, 337, 339, 352, 354

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

F. Iacobescu, Smarandache Partition Type and Other Sequences, Bull. Pure Appl. Sci. 16E, 237-240, 1997.

Eric Weisstein's World of Mathematics, Nonarithmetic Progression Sequence

Index entries related to non-averaging sequences

Formula

a(n) = (3-n)/2 + 2*floor(n/2) + Sum_{k=1..n-1} 3^A007814(k)/2 = A003278(n) + [n is even], proved by Lawrence Sze, following a conjecture by Ralf Stephan.

a(n) = b(n-1), with b(0)=1, b(2n) = 3b(n) - 2 - 3[n odd], b(2n+1) = 3b(n)-3[n odd].

Maple

a:= proc(n) local m, r, b; m, r, b:= n-1, 2-irem(n, 2), 1;
      while m>0 do r:= r+b*irem(m, 2, 'm'); b:= b*3 od; r
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Nov 02 2021

Mathematica

Select[Range[1000], MatchQ[IntegerDigits[#-1, 3], {(0|1)..., 0|2}]&] (* Jean-François Alcover, Jan 13 2019, after Tanya Khovanova in A186776 *)

Prog

(PARI) v[1]=1; v[2]=3; for(n=3, 1000, f=2; m=v[n-1]+1; while(1, forstep(k=n-1, 1, -1, if(v[k]<(m+1)/2, f=1; break); for(l=1, k-1, if(m-v[k]==v[k]-v[l], f=0; break)); if(f<2, break)); if(!f, m=m+1; f=2); if(f==1, break)); v[n]=m) \\ Ralf Stephan
(PARI) a(n)=if(n<1, 1, if(n%2==0, 3*a(n/2)-2-3*((n/2)%2), 3*a((n-1)/2)-3*(((n-1)/2)%2))) \\ Ralf Stephan

Crossrefs

Equals A186776(n)+1, A033160(n)-1, A033163(n)-2.

Cf. A092482, A185256.

Row 1 of array in A093682.

Sequence in context: A322457 A137951 A082694 * A336909 A031132 A322165

Adjacent sequences: A004790 A004791 A004792 * A004794 A004795 A004796

Keyword

nonn

Author

N. J. A. Sloane, Clark Kimberling

Extensions

Rechecked by David W. Wilson, Jun 04 2002

Status

approved