A033157 Begins with (1, 4); avoids 3-term arithmetic progressions.

1, 4, 5, 8, 10, 13, 14, 17, 28, 31, 32, 35, 37, 40, 41, 44, 82, 85, 86, 89, 91, 94, 95, 98, 109, 112, 113, 116, 118, 121, 122, 125, 244, 247, 248, 251, 253, 256, 257, 260, 271, 274, 275, 278, 280, 283, 284, 287, 325, 328, 329, 332, 334, 337, 338, 341, 352, 355, 356, 359, 361

Offset

1,2

Comments

Also called Stanley Sequence S[1,4]. - Ralf Stephan, Jan 31 2014

References

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

H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.

Links

Table of n, a(n) for n=1..61.

Eric Weisstein's World of Mathematics, Nonarithmetic Progression Sequence

Index entries related to non-averaging sequences

Formula

Partial sums of Da(n), where Da(n) is defined in the PARI program.

a(n) = A004793(n) + [n is even] + [ceiling(n/2) is even]. Proof by Lawrence Sze. - Ralf Stephan, Nov 15 2004

a(n) = A033161(n) - 1 = A185256(n) + 1. - Ralf Stephan, Jan 31 2014

Prog

(PARI) Da(n)=if(n<1, 1, if(n%2==0, 3*Da(n/2)+5-13*((n/2)%2)-6*((n/2)%4==2), 3)) /* Ralf Stephan */

Crossrefs

Cf. A092482, A004793. Row 2 of array in A093682.

Sequence in context: A304108 A214026 A174396 * A310574 A059659 A140459

Adjacent sequences: A033154 A033155 A033156 * A033158 A033159 A033160

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved