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 A020654 Lexicographically earliest infinite increasing sequence of nonnegative numbers containing no 5-term arithmetic progression. 49
 0, 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 43, 50, 51, 52, 53, 55, 56, 57, 58, 60, 61, 62, 63, 65, 66, 67, 68, 75, 76, 77, 78, 80, 81, 82, 83, 85, 86, 87, 88, 90, 91, 92, 93, 125, 126, 127 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This is also the set of numbers with no "4" in their base-5 representation. In fact, for any prime p, the sequence consisting of numbers with no (p-1) in their base-p expansion is the same as the earliest sequence containing no p-term arithmetic progression. - Nathaniel Johnston, Jun 26-27 2011 LINKS Nathaniel Johnston, Table of n, a(n) for n = 1..10000 J. L. Gerver and L. T. Ramsey, Sets of integers with no long arithmetic progressions generated by the greedy algorithm, Math. Comp., 33 (1979), 1353-1359. Samuel S. Wagstaff, Jr., On k-free sequences of integers, Math. Comp., 26 (1972), 767-771. MAPLE seq(`if`(numboccur(4, convert(n, base, 5))=0, n, NULL), n=0..127); # Nathaniel Johnston, Jun 27 2011 MATHEMATICA Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 5 ], 4 ]==0)& ] PROG (PARI) is(n)=while(n>4, if(n%5==4, return(0)); n\=5); 1 \\ Charles R Greathouse IV, Feb 12 2017 (Python) from sympy.ntheory.factor_ import digits print([n for n in range(201) if digits(n, 5)[1:].count(4)==0]) # Indranil Ghosh, May 23 2017 (Julia) function a(n)     m, r, b = n, 0, 1     while m > 0         m, q = divrem(m, 4)         r += b * q         b *= 5     end r end; [a(n) for n in 0:66] |> println # Peter Luschny, Jan 03 2021 CROSSREFS Cf. A023717. Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first): 3-term AP: A005836 (>=0), A003278 (>0); 4-term AP: A005839 (>=0), A005837 (>0); 5-term AP: A020654 (>=0), A020655 (>0); 6-term AP: A020656 (>=0), A005838 (>0); 7-term AP: A020657 (>=0), A020658 (>0); 8-term AP: A020659 (>=0), A020660 (>0); 9-term AP: A020661 (>=0), A020662 (>0); 10-term AP: A020663 (>=0), A020664 (>0). Sequence in context: A087069 A023737 A037459 * A182777 A214988 A028804 Adjacent sequences:  A020651 A020652 A020653 * A020655 A020656 A020657 KEYWORD nonn,easy,changed AUTHOR EXTENSIONS Added "infinite" to definition. - N. J. A. Sloane, Sep 28 2019 STATUS approved

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Last modified January 17 01:29 EST 2021. Contains 340213 sequences. (Running on oeis4.)