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%I A280706 #13 Mar 23 2017 11:43:26
%S A280706 1,2,3,4,6,8,10,13,16,19,23,26,30,35,39,44,49,54,60,66,72,78,86,92,
%T A280706 100,108,116,124,132,142,150,159,169,179,189,200,211,221,232,243,254,
%U A280706 266,278,290,302,314,330,340,354,368,380,394,410,424,438,454,468,484,500,516,532,552,568,585,606,622,639,658,678,698,719,740
%N A280706 a(n) = Sum_{k=1..n} q(k+1-q(k)), where q(k) = A005185(k); partial sums of A283467.
%H A280706 Antti Karttunen, <a href="/A280706/b280706.txt">Table of n, a(n) for n = 1..10001</a>
%H A280706 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%F A280706 a(1) = 1, for > 1, a(n) = A283467(n) + a(n-1).
%F A280706 A284173(n) = a(n) modulo n.
%t A280706 a[1] = a[2] = 1; a[n_] := a[n] = a[n - a[n - 1]] + a[n - a[n - 2]]; Accumulate@ Table[a[n + 1 - a[n]], {n, 72}] (* _Michael De Vlieger_, Mar 22 2017 *)
%o A280706 (Scheme)
%o A280706 ;; Code for A005185 given under that entry.
%o A280706 ;; With memoization-macro definec:
%o A280706 (definec (A280706 n) (if (= 1 n) 1 (+ (A280706 (- n 1)) (A283467 n))))
%o A280706 ;; As an explicit sum (slower):
%o A280706 (define (A280706 n) (add (lambda (k) (A005185 (- (+ k 1) (A005185 k)))) 1 n))
%o A280706 ;; Implements sum_{i=lowlim..uplim} intfun(i)
%o A280706 (define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))
%o A280706 (PARI) a(n) = if(n<3, 1, a(n - a(n - 1)) + a(n - a(n - 2)));
%o A280706 for(n=1, 72, print1(sum(k=1, n, a(k + 1 - a(k))),", ")) \\ _Indranil Ghosh_, Mar 22 2017
%Y A280706 Cf. A005185, A284173.
%Y A280706 Partial sums of A283467.
%K A280706 nonn
%O A280706 1,2
%A A280706 _Antti Karttunen_ after _Altug Alkan_'s A284173, Mar 22 2017

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