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 A253671 a(n) = floor(A000111(n+1)/A000111(n)). 1
 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 40, 40 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 1, 2, 3, 4, ... first appear at n = 1, 3, 5, 7, 8, 10, 11, 13, ... . a(500) = 318. Numbers appearing only once: interleave 4+7*n, 6+7*n, 9+7*n = 4, 6, 9, 11, 13, 16, ... . This is a nondecreasing sequence. The ratio a(n)/n asymptotically tends to 7/11 = 0.6363... - Jean-François Alcover, Jul 21 2015 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,1,-1). FORMULA a(n+2) = a(n+1) + (0, 1, 0, followed by a sequence of period 11: repeat 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1). a(n+12) = a(n+1) + (6, 7, 6, followed by 7's = A010727). a(n) = a(n-1) + a(n-11) - a(n-12) for n>15. - Colin Barker, Jan 22 2015 G.f.: x*(x^14-x^13+x^12-x^11+x^10+x^9+x^7+x^6+x^4+x^2+1) / ((x-1)^2*(x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)). - Colin Barker, Jan 22 2015 EXAMPLE Floor of 1/1, 1/1, 2/1, 5/2, 16/5, 61/16, ... . 1=1*1+0, 1=1*1+0, 2=2*1+0, 5=2*2+1, 16=3*5+1, 61=3*16+13, 272=4*61+28, ... . MATHEMATICA max = 500; ee = Table[2^n*EulerE[n, 1] + EulerE[n] - 1, {n, 0, max}]; A000111 = Table[Differences[ee, n] // First // Abs, {n, 0, max}]; Table[Quotient[A000111[[n + 1]], A000111[[n]]], {n, 1, max}] (* Jean-François Alcover, Jan 08 2015 *) PROG (PARI) Vec(x*(x^14-x^13+x^12-x^11+x^10+x^9+x^7+x^6+x^4+x^2+1)/((x-1)^2*(x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)) + O(x^100)) \\ Colin Barker, Jan 22 2015 (Python) # requires python 3.2 or higher from itertools import accumulate A253671_list, blist, l1, l2 = [1], [1], 1, 1 for n in range(10**2): ....blist = list(reversed(list(accumulate(reversed(blist))))) + [0] if n % 2 else [0]+list(accumulate(blist)) ....l2, l1 = l1, sum(blist) ....A253671_list.append(l1//l2) # Chai Wah Wu, Jan 29 2015 CROSSREFS Cf. A000111, A010727, A017005, A017029, A017053. Sequence in context: A029092 A280814 A319433 * A209081 A248610 A168581 Adjacent sequences:  A253668 A253669 A253670 * A253672 A253673 A253674 KEYWORD nonn,easy AUTHOR Paul Curtz, Jan 08 2015, with the help of Jean-François Alcover. STATUS approved

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Last modified January 16 06:48 EST 2021. Contains 340204 sequences. (Running on oeis4.)