The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A339932 a(n+1) = a(n-4-a(n)^2) + 1, starting with a(1) = a(2) = a(3) = a(4) = a(5) = 0. 3
 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 4, 4, 3, 5, 3, 5, 3, 5, 3, 4, 5, 3, 5, 4, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS To obtain the next term, square the current term and add 4, then count back this number and add 1. The sequence cannot repeat. Proof: Assume a finite period. Label an arbitrary term in the period x. Because of the back-referencing definition it follows that x-1 has to be in the period, and by the same argument so does x-2 and x-3, x-4,... until 0. But it is not possible to obtain new 0s since each new term is larger than one already existing term. Every positive integer appears in the sequence. First occurrence of n: 1, 6, 12, 21, 35, 49, 70, 100, 130, 171, 212, 266, 320, 406, 564, 669, 849,... The sequence appears to grow with the cube root of n, which is expected since f(x) = (3*x)^(1/3) satisfies the definition for large x, i.e. lim_{x->oo} f(x+1)-(f(x-4-f(x)^2)+1) = 0. The width of the distribution of terms within a range (n^2,n^2+n) appears to be constant for large n and can be defined as: lim_{n->oo} ( 1/n*Sum_{k=n..2n} ( Max_{i=k^2..k^2+k} a(i) - Min_{i=k^2..k^2+k} a(i) ) ) and evaluates to 8.10... (for n^2 = 5*10^8). LINKS FORMULA a(n) ~ (3*n)^(1/3) (conjectured). EXAMPLE a(6) = a(5-4-a(5)^2)+1 = a(1)+1 = 1. a(7) = a(6-4-a(6)^2)+1 = a(1)+1 = 1. a(8) = a(7-4-a(7)^2)+1 = a(2)+1 = 1. a(9) = a(8-4-a(8)^2)+1 = a(3)+1 = 1. a(10) = a(9-4-a(9)^2)+1 = a(4)+1 = 1. a(11) = a(10-4-a(10)^2)+1 = a(5)+1 = 1. a(12) = a(11-4-a(11)^2)+1 = a(6)+1 = 2. PROG (Python) a = [0, 0, 0, 0, 0] for n in range(4, 1000): a.append(a[n-4-a[n]**2]+1) (C) #include #include int main(void){ int N = 1000; int *a = (int*)malloc(N*sizeof(int)); a[0] = 0; a[1] = 0; a[2] = 0; a[3] = 0; a[4] = 0; for(int n = 4; n < N-1; ++n){ a[n+1] = a[n-4-a[n]*a[n]]+1; } free(a); return 0; } CROSSREFS Analogous sequences: A339929, A339930, A339931. Cf. A330772, A005206, A002516, A062039. Sequence in context: A036485 A331971 A030547 * A254690 A156642 A155124 Adjacent sequences: A339929 A339930 A339931 * A339933 A339934 A339935 KEYWORD nonn AUTHOR Rok Cestnik, Dec 23 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 11:09 EST 2022. Contains 358493 sequences. (Running on oeis4.)