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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

• Eric Weisstein's World of Mathematics, Nonarithmetic Progression Sequence
• Index entries related to non-averaging sequences

Crossrefs

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

Programs

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 */

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