A079257 -id:A079257 - cp's OEIS frontend

A092875 Aronson transform of the "evil" sequence (A001969).

2, 3, 5, 7, 9, 11, 12, 13, 15, 16, 17, 18, 20, 21, 23, 24, 27, 29, 31, 33, 34, 35, 36, 39, 41, 42, 43, 44, 45, 47, 48, 49, 51, 53, 54, 57, 59, 61, 63, 64, 65, 66, 68, 71, 72, 73, 75, 77, 78, 79, 80, 81, 83, 85, 87, 88, 89, 91, 92, 93, 95, 97, 99, 101, 102, 105, 107, 108, 109

Offset: 1

Ferenc Adorjan (fadorjan(AT)freemail.hu)

b(n) positive monotonic sequence is the Aronson transform of a(n) positive monotonic sequence if every member of a(n) satisfies the condition: "k is in b if and only if b(k) is in a", so that k must be the least such number.

F. Adorjan, Binary mapping of monotonic sequences and the Aronson function
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.

Cf. A079254, A079257, A079258, A080760.

{arons(v)= /* Returns the Aronson transform of v */ local(x=[],pv=1,px=1,n=1,i=0,k,l); l=matsize(v)[2];
/*The initial terms: */ if(n0 if (i+1) is in v */ if(k==i,n+=1;if(pv<0,pv=abs(pv);while(pv>0,n+=1;pv=isin (n,v,l,pv))), px=isin(i+1,x,i,px);if(px>0,pv=-abs(pv);while (pv<0,n+=1;pv=isin(n,v,l,pv)), pv=abs(pv);while(pv>0,n+=1;pv=isin(n,v,l,pv)))); x=concat(x,n);i+=1);/*print(i);*/ return(x) }
{isin(x,v,l,poi)= /*If x integer is in v monotonic vector of length l, the function returns a positive 'poi', else a negative one. (poi is pointer, used for acceleration. The last returned value is recommended in the input) */
poi=abs(poi);if(poi==1&&x1,poi-=1);if(x<>v [poi],poi*=-1), if(x>v[poi], while(x>v[poi]&&poiv [poi],poi*=-1)));return(poi))}

A079258 a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) is a square".

Original entry on oeis.org

0, 1, 3, 4, 9, 10, 11, 12, 13, 16, 25, 36, 49, 64, 65, 66, 81, 82, 83, 84, 85, 86, 87, 88, 89, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153

Offset: 0

N. J. A. Sloane and Matthew Vandermast, Feb 04 2003

Also, a(n) is smallest nonnegative integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = n^2.

Ivan Neretin, Table of n, a(n) for n = 0..10000
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)
Index entries for sequences of the a(a(n)) = 2n family

See A079000, A079253, A079254, A079256, A079257 for similar sequences.

a = {1, 3}; Do[AppendTo[a, If[MemberQ[a, n], Position[a, n][[1, 1]]^2, a[[-1]] + 1]], {n, 3, 58}]; Prepend[a, 0] (* Ivan Neretin, Jul 09 2015 *)

A242940 a(n) is the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a term of the sequence if and only if a(n) is a Fibonacci number".

Original entry on oeis.org

1, 2, 3, 6, 7, 8, 13, 21, 22, 23, 24, 25, 34, 35, 36, 37, 38, 39, 40, 41, 55, 89, 144, 233, 377, 378, 379, 380, 381, 382, 383, 384, 610, 987, 1597

Offset: 1

J. Lowell, Jun 12 2014

			a(4) cannot be 5 because that would require 4 to be a term of this sequence.

Cf. A079000, A079253, A079254, A079258, A079256, A079257.

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A092875 Aronson transform of the "evil" sequence (A001969).

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A079258 a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) is a square".

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A242940 a(n) is the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a term of the sequence if and only if a(n) is a Fibonacci number".

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