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 A113880 Variation on Recamán's sequence utilizing the four basic operations (/,-,+,*) in that order. 1
 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, 407, 381, 354, 326, 297, 267, 236, 204, 171, 137, 102, 66, 29, 67, 28, 68, 27, 69, 26, 70, 115, 161, 114, 162, 113, 163, 112, 60, 3180, 3126, 3071, 3015, 2958, 51, 110, 50, 111, 49 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS More precisely: a(n) = a(n-1)/n if a(n-1)/n is integer and not already in the sequence. Else: a(n) = a(n-1)-n if a(n-1)-n is positive and not already in the sequence. Else: a(n) = a(n-1)+n if a(n-1)+n is not already in the sequence. Else: a(n) = a(n-1)*n if a(n-1)*n is not already in the sequence. Else STOP. In other words, divide if you can, else subtract, else add, else multiply. 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? At a(2500000000)=2285684529311288243, there have been 44 divisions, 2499821613 subtractions, 178253 additions, and 90 multiplications. The largest value seen was a=3555357710450807490. No multiplication step has produced a duplicate term. - Benjamin Chaffin, Sep 22 2016 LINKS Robert G. Wilson v, Table of n, a(n) for n = 0..10000 EXAMPLE a(24) = 432 because: a(23) = 18. 18/24 is not an integer. 18-24 is negative. 18 + 24 = 42 is already in the sequence. Therefore 18 * 24 = 432. MATHEMATICA 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 *) CROSSREFS Cf. A005132. Sequence in context: A064389 A118201 A274647 * A339192 A171884 A339557 Adjacent sequences:  A113877 A113878 A113879 * A113881 A113882 A113883 KEYWORD nonn AUTHOR Sergio Pimentel, Jan 27 2006 EXTENSIONS a(0)=0 prepended by Robert G. Wilson v, Sep 10 2016 STATUS approved

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Last modified April 22 19:11 EDT 2021. Contains 343177 sequences. (Running on oeis4.)