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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. 18
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

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

LINKS

Table of n, a(n) for n=1..58.

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].

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: A047296 A137951 A082694 * A031132 A057477 A249666

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

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Last modified February 20 16:25 EST 2018. Contains 299380 sequences. (Running on oeis4.)