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A033157
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Begins with (1, 4); avoids 3-term arithmetic progressions.
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13
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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
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OFFSET
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1,2
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COMMENTS
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Also called Stanley Sequence S[1,4]. - Ralf Stephan, Jan 31 2014
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REFERENCES
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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.
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LINKS
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FORMULA
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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
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PROG
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(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 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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