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%I #45 May 26 2023 08:50:42
%S 0,1,3,6,2,7,13,20,12,21,11,22,10,23,9,24,8,25,43,62,42,63,41,18,432,
%T 407,381,354,326,297,267,236,204,171,137,102,66,29,67,28,68,27,69,26,
%U 70,115,161,114,162,113,163,112,60,3180,3126,3071,3015,2958,51,110,50,111,49
%N Variation on Recamán's sequence utilizing the four basic operations (/,-,+,*) in that order.
%C More precisely:
%C a(n) = a(n-1)/n if a(n-1)/n is integer and not already in the sequence. Else:
%C a(n) = a(n-1)-n if a(n-1)-n is positive and not already in the sequence. Else:
%C a(n) = a(n-1)+n if a(n-1)+n is not already in the sequence. Else:
%C a(n) = a(n-1)*n if a(n-1)*n is not already in the sequence. Else STOP.
%C In other words, divide if you can, else subtract, else add, else multiply.
%C By a(1000) there are 3 division steps, 928 subtraction steps, 59 addition steps and 10 multiplication steps. It is unlikely that every number belongs to the sequence since there are many "holes". It is an open question if there are any repetitions after a multiplication step. Can anybody expand the series?
%C At a(2500000000) = 2285684529311288243, there have been 44 divisions, 2499821613 subtractions, 178253 additions, and 90 multiplications. The largest value seen was a(1926305697) = 3555357710450807490. No multiplication step has produced a duplicate term. - _Benjamin Chaffin_, Sep 22 2016
%H Robert G. Wilson v, <a href="/A113880/b113880.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rea#Recaman">Index entries for sequences related to Recamán's sequence</a>
%e a(24) = 432 because:
%e - a(23) = 18,
%e - 18/24 is not an integer,
%e - 18 - 24 is negative,
%e - 18 + 24 = 42 is already in the sequence,
%e - 18 * 24 = 432 is not already in the sequence.
%t f[s_List] := Block[{l = s[[-1]], n = Length@ s}, If[ IntegerQ[l/n] && !MemberQ[s, l/n], Append[s, l/n], If[l > n && !MemberQ[s, l - n], Append[s, l - n], If[ !MemberQ[s, l + n], Append[s, l + n], Append[s, l*n]]]]]; Nest[f, {0}, 62] (* _Robert G. Wilson v_, Sep 10 2016 *)
%o (Python)
%o from itertools import count, islice
%o def A113880(): # generator of terms
%o aset, an = {0, 1}, 1
%o yield from [0, 1]
%o for n in count(2):
%o q, r = divmod(an, n)
%o if r == 0 and q not in aset: an = q
%o elif (d:=an-n) > 0 and d not in aset: an = d
%o elif (s:=an+n) not in aset: an = s
%o elif (m:=an*n) not in aset: an = m
%o else: return
%o yield an
%o aset.add(an)
%o print(list(islice(A113880(), 63))) # _Michael S. Branicky_, May 26 2023
%Y Cf. A005132.
%K nonn
%O 0,3
%A _Sergio Pimentel_, Jan 27 2006
%E a(0) = 0 prepended by _Robert G. Wilson v_, Sep 10 2016
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