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%I #18 Aug 15 2018 01:12:55
%S 16,17,18,13,14,15,16,17,18,13,14,15,16,17,18,13,14,15,16,17,18,13,14,
%T 15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
%U 38,39,40
%N Generalized McCarthy function: a(n) = n - s if n > c; otherwise, a(n) = a(a(n+t)) with d = t - s > 0, with parameters t=15, s=9, c=21.
%C The parameters t=11, s=10, c=100 give the McCarthy 91-Function A103847.
%F The sequence begins with a(1) = d*floor((c+d-1)/d) + 1 - s;
%F if n <= c and c > d then a(n) = a(n-d);
%F if n <= c <= d then a(n) = a(1) + n - 1;
%F if n > c then a(n) = n - s.
%e For t=9, s=5, d=t-s=4, and
%e c=1: (0,-3,-2,-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...)
%e c=2: (0, 1,-2,-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...)
%e c=3: (0, 1, 2,-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...)
%e c=4: (0, 1, 2, 4, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...)
%e c=5: (4, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...)
%e c=6: (4, 5, 2, 3, 4, 5, 2, 3, 4, 5, 6, 7, 8, 9, ...)
%e c=7: (4, 5, 6, 3, 4, 5, 6, 3, 4, 5, 6, 7, 8, 9, ...)
%e c=8: (4, 5, 6, 7, 4, 5, 6, 7, 4, 5, 6, 7, 8, 9, ...)
%e c=9: (8, 5, 6, 7, 8, 5, 6, 7, 8, 5, 6, 7, 8, 9, ...)
%p d=t-s:
%p a[1]:=d*(iquo(c+d-1,d))+1-s:
%p if (c <= d) then
%p for j from 2 to c do
%p a[j]:=a[1]+j-1:
%p end do:
%p end if:
%p if (c > d) then
%p k:=(c-1) mod d +1:
%p for j from 2 to k do
%p a[j]:=a[1]+j-1:
%p end do:
%p for j from (k+1) to d do
%p a[j]:=a[1]+j-d-1:
%p end do:
%p for j from (d+1) to c do
%p a[j]:=a[j-d]:
%p end do:
%p end if:
%p for n from (c+1) to 50 do
%p a[n]:=n-s:
%p end do:
%Y Cf. A103847 (McCarthy 91-function).
%K nonn
%O 1,1
%A _Paul Weisenhorn_, May 13 2011
%E Name corrected by _Paul Weisenhorn_, Aug 12 2018
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