A005050 -id:A005050 - cp's OEIS frontend

A005048 Minimal span of set of n elements with no 4-term arithmetic progression.

4, 5, 7, 8, 9, 12, 14, 16, 18, 20, 22, 24, 26, 27, 29, 32, 33, 36, 39, 42, 44, 47, 49, 52, 53, 57, 59, 63, 65, 67, 69, 73, 76, 78, 81, 83, 86, 90, 92, 96, 98, 100, 103, 104, 106, 111, 113, 119, 121, 125, 128, 131, 133, 137, 140

Offset: 4

N. J. A. Sloane

If the first appearance of n in A003003 is A003003(k) = n, then a(n) = k-1. - Robert Israel, Mar 21 2016

			Example for n=13: { 1, 2, 3, 5, 6, 8, 9, 10, 16, 17, 18, 20, 21 } with span 20.

B. E. Brown and D. M. Gordon, On sequences without geometric progressions, Math. Comp. 65 (1996), no. 216, 1749-1754.
Sean A. Irvine, Example sets for a(4)-a(27)

Cf. A005047, A005049, A005050.

Corrected and extended by David W. Wilson, May 15 1997
a(22)-a(26) from Sean A. Irvine, Mar 17 2016
a(24)-a(26) corrected by Robert Israel, Mar 20 2016
a(27) from Sean A. Irvine, Mar 20 2016
a(28)-a(34) from Robert Israel, Mar 21 2016
a(35)-a(58) from Fausto A. C. Cariboni, Jun 17 2018

A005049 Minimal span of set of n elements with no 5-term arithmetic progression.

Original entry on oeis.org

5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 23, 24, 26, 27, 28, 30, 32, 33, 35, 36, 37, 38, 40, 41, 42, 43, 48, 50, 51, 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, 104, 108, 112

Offset: 5

N. J. A. Sloane

If the first appearance of n in A003004 is A003004(k) = n, then a(n) = k-1. - Fausto A. C. Cariboni, Jun 17 2018

B. E. Brown and D. M. Gordon, On sequences without geometric progressions, Math. Comp. 65 (1996), no. 216, 1749-1754.
Sean A. Irvine, Example sets for a(5)-a(34)

Cf. A005047, A005048, A005050.

More terms from David W. Wilson, May 15 1997
a(24)-a(34) from Sean A. Irvine, Mar 16 2016
a(33) corrected by Fausto A. C. Cariboni, Jun 17 2018
a(35)-a(67) from Fausto A. C. Cariboni, Jun 17 2018

A242823 Perimeter (rounded down) of Pi-shaped box fractal after n iterations.

Original entry on oeis.org

1, 2, 5, 15, 39, 103, 269, 700, 1821, 4736, 12313, 32016, 83242, 216429, 562716, 1463063, 3803966, 9890311, 25714810, 66858508, 173832121, 451963515, 1175105140, 3055273364, 7943710747, 20653647942, 53699484649

Offset: 0

Kival Ngaokrajang, May 23 2014

nonn

Let 13 boxes be placed into a 5 X 5 square grid, arranged in the shape of a capital letter Pi (see illustration). Also let the initial side length of a box = 1/28. The side length of a box after n iterations will be 1/(4*A005050(n)) i.e., 1/28, 1/140, 1/700, 1/3500, ... The sides count (any lengths) is 12*A001019(n), i.e., 12, 108, 972, 8748, ... The Hausdorff dimension = log(13)/log(5) = 1.593692641167... or A154265.

Kival Ngaokrajang, Illustration of initial terms
Eric Weisstein's World of Mathematics, Box Fractal
Wikipedia, Vicsek fractal

Cf. A001019, A005050, A154265.

{a=28;b=1;print1(1,", "); for (n=2,50, b=b*0.2; a=(a*13-16*2^(n-1)-8); print1(floor(a*b/28),", "))}

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A005048 Minimal span of set of n elements with no 4-term arithmetic progression.

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A005049 Minimal span of set of n elements with no 5-term arithmetic progression.

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A242823 Perimeter (rounded down) of Pi-shaped box fractal after n iterations.

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