A190582 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.

16, 17, 18, 13, 14, 15, 16, 17, 18, 13, 14, 15, 16, 17, 18, 13, 14, 15, 16, 17, 18, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40

Offset

1,1

Comments

The parameters t=11, s=10, c=100 give the McCarthy 91-Function A103847.

Links

Table of n, a(n) for n=1..49.

Formula

The sequence begins with a(1) = d*floor((c+d-1)/d) + 1 - s;

if n <= c and c > d then a(n) = a(n-d);

if n <= c <= d then a(n) = a(1) + n - 1;

if n > c then a(n) = n - s.

Example

For t=9, s=5, d=t-s=4, and
  c=1: (0,-3,-2,-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...)
  c=2: (0, 1,-2,-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...)
  c=3: (0, 1, 2,-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...)
  c=4: (0, 1, 2, 4, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...)
  c=5: (4, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...)
  c=6: (4, 5, 2, 3, 4, 5, 2, 3, 4, 5, 6, 7, 8, 9, ...)
  c=7: (4, 5, 6, 3, 4, 5, 6, 3, 4, 5, 6, 7, 8, 9, ...)
  c=8: (4, 5, 6, 7, 4, 5, 6, 7, 4, 5, 6, 7, 8, 9, ...)
  c=9: (8, 5, 6, 7, 8, 5, 6, 7, 8, 5, 6, 7, 8, 9, ...)

Maple

d=t-s:
a[1]:=d*(iquo(c+d-1, d))+1-s:
if (c <= d) then
  for j from 2 to c do
    a[j]:=a[1]+j-1:
  end do:
end if:
if (c > d) then
  k:=(c-1) mod d +1:
  for j from 2 to k do
    a[j]:=a[1]+j-1:
  end do:
  for j from (k+1) to d do
    a[j]:=a[1]+j-d-1:
  end do:
  for j from (d+1) to c do
    a[j]:=a[j-d]:
  end do:
end if:
for n from (c+1) to 50 do
  a[n]:=n-s:
end do:

Crossrefs

Cf. A103847 (McCarthy 91-function).

Sequence in context: A070575 A004505 A262460 * A004457 A248501 A115420

Adjacent sequences: A190579 A190580 A190581 * A190583 A190584 A190585

Keyword

nonn

Author

Paul Weisenhorn, May 13 2011

Extensions

Name corrected by Paul Weisenhorn, Aug 12 2018

Status

approved