A080760 -id:A080760 - 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))}

A080746 Inverse Aronson transform of lower Wythoff sequence A000201.

Original entry on oeis.org

1, 4, 6, 7, 9, 10, 12, 14, 15, 17, 19, 20, 22, 23, 25, 27, 28, 30, 31, 33, 35, 36, 38, 40, 41, 43, 44, 46, 48, 49, 51, 53, 54, 56, 57, 59, 61, 62, 64, 65, 67, 69, 70, 72, 74, 75, 77, 78, 80, 82, 83, 85, 86, 88, 90, 91, 93, 95, 96, 98, 99

Offset: 1

Matthew Vandermast, Mar 08 2003

nonn

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)

Union of A003622 and A035336, omitting 2. Cf. A000201, A080760.

Same as A026273 except for initial terms.

Consists of numbers [phi[phi*k]] (k >= 1) and [phi[phi^2*k]]-1 (k >= 2), where phi = (1+sqrt(5))/2. - N. J. A. Sloane, Mar 10 2003

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI