A079354 a(1)=1; a(n)=a(n-1)-1 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.
1, 4, 7, 6, 9, 8, 7, 6, 5, 8, 11, 14, 17, 16, 19, 18, 17, 16, 15, 18, 21, 24, 27, 26, 29, 28, 27, 26, 25, 28, 31, 34, 37, 36, 39, 38, 37, 36, 35, 38, 41, 44, 47, 46, 49, 48, 47, 46, 45, 48, 51, 54, 57, 56, 59, 58, 57, 56, 55, 58, 61, 64, 67, 66, 69, 68, 67, 66, 65, 68, 71, 74, 77
Offset: 1
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
- Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See p. 2.
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).
Programs
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Mathematica
LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{1,4,7,6,9,8,7,6,5,8,11},80] (* Harvey P. Dale, Feb 01 2015 *) -
PARI
Vec(x*(2*x^10+3*x^9-x^8-x^7-x^6-x^5+3*x^4-x^3+3*x^2+3*x+1)/(x^11-x^10-x+1) + O(x^100)) \\ Colin Barker, Oct 16 2013
Formula
a(n)-n is periodic with period (0, 2, 4, 2, 4, 2, 0, -2, -4, -2) of length 10.
a(10t+i) = 10t+c_i, 1<=i<=10, c_i=(1, 4, 7, 6, 9, 8, 7, 6, 5, 8). a(n) = n iff n == 1 or 7 (mod 10).
G.f.: x*(2*x^10+3*x^9-x^8-x^7-x^6-x^5+3*x^4-x^3+3*x^2+3*x+1) / (x^11-x^10-x+1). - Colin Barker, Oct 16 2013
Comments