The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A065186 a(1)=1, a(2)=3, a(3)=5, a(4)=2, a(5)=4; for n > 5, a(n) = a(n-5) + 5. 7
 1, 3, 5, 2, 4, 6, 8, 10, 7, 9, 11, 13, 15, 12, 14, 16, 18, 20, 17, 19, 21, 23, 25, 22, 24, 26, 28, 30, 27, 29, 31, 33, 35, 32, 34, 36, 38, 40, 37, 39, 41, 43, 45, 42, 44, 46, 48, 50, 47, 49, 51, 53, 55, 52, 54, 56, 58, 60, 57, 59, 61, 63, 65, 62, 64, 66, 68, 70, 67, 69, 71, 73 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS "Greedy Dragons" permutation of the natural numbers, inverse of A065187. This permutation is produced by a simple greedy algorithm: walk along each successive antidiagonal of an infinite array and place a Shoogi dragon piece (i.e., the "promoted" rook, Ryuu, that moves like a chess rook, but can also move one square diagonally) in the first available position where it is not threatened by any dragon already placed. I.e., this permutation satisfies the condition that p(i+1) != p(i)+-1 for all i. Alternatively, this is obtained directly if n-1 is converted to base 5, the least significant digit is doubled (modulo 5, i.e., 0->0, 1->2, 2->4, 3->1, 4->3) and one is added back to the resulting number. a(1) = 1, a(n) = smallest number such that no two successive terms differ by 1. - Amarnath Murthy, May 06 2003 This is also the lexicographic first positive sequence such that the distance between any subsequent terms, |a(n+1)-a(n)|, is a prime number and no number occurs twice, with a(1) = 1: A variant of A277618, which obeys the same rules but starts with a(0) = 0; and of A277617, which is defined similarly with squares > 1 instead of primes. - M. F. Hasler, Oct 23 2016 LINKS Harry J. Smith, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 1, -1). FORMULA a(n) = n + ((n-1) mod 5) - 5*(floor(((n-1) mod 5)/3)). G.f.: x*(x^5 + 2*x^4 - 3*x^3 + 2*x^2 + 2*x + 1)/((x - 1)*(x^5 - 1)) a(n) = a(n-1) + a(n-5) - a(n-6), with n>6, a(1)=1, a(2)=3, a(3)=5, a(4)=2, a(5)=4, a(6)=6. - Harvey P. Dale, Mar 11 2012 MAPLE [seq(GreedyDragonsDirect(j), j=1..125)]; GreedyDragonsDirect := n -> n + ((n-1) mod 5) - 5*(floor((n-1 mod 5)/3)); Or empirically, by using the algorithm given at A065188: GreedyDragons := upto_n -> PM2PL(GreedyNonThreateningPermutation(upto_n, 1, 1), upto_n); MATHEMATICA RecurrenceTable[{a == 1, a == 3, a == 5, a == 2, a == 4, a[n] == a[n - 5] + 5}, a, {n, 80}] (* or *) LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 3, 5, 2, 4, 6}, 80] (* Harvey P. Dale, Mar 11 2012 *) Flatten[Table[5n + {1, 3, 5, 2, 4}, {n, 0, 14}]] (* Alonso del Arte, Jul 25 2017 *) PROG (PARI) { for (n=1, 1000, if (n>5, a=a5 + 5; a5=a4; a4=a3; a3=a2; a2=a1; a1=a, if (n==1, a=a5=1, if (n==2, a=a4=3, if (n==3, a=a3=5, if (n==4, a=a2=2, a=a1=4))))); write("b065186.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 13 2009 (PARI) n=1; v=[n]; while(n<200, if(isprime(abs(n-v[#v]))&&!vecsearch(vecsort(v), n), v=concat(v, n); n=1); n++); v \\ Derek Orr, Jul 24 2017 (PARI) a(n) = n--; [1, 3, 5, 2, 4][n%5+1]+5*(n\5) \\ David A. Corneth, Jul 24 2017 (PARI) first(n) = my(v = [1, 3, 5, 2, 4]); if(n < 5, return(vector(n, i, v[i])), v = concat(v, vector(n-5))); for(i=6, n, v[i]=5 + v[i-5]); v \\ David A. Corneth, Jul 24 2017 (PARI) nxt(n) = if(n%5, n+2, n-3) \\ David A. Corneth, Jul 24 2017 CROSSREFS "Greedy Queens" and "Quintal Queens" permutations: A065188, A065257. Cf. A065186. Sequence in context: A104807 A309492 A131793 * A210521 A219249 A203553 Adjacent sequences:  A065183 A065184 A065185 * A065187 A065188 A065189 KEYWORD nonn,easy AUTHOR Antti Karttunen, Oct 19 2001 STATUS approved

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

Last modified November 28 00:12 EST 2021. Contains 349395 sequences. (Running on oeis4.)