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

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Keywords

• easy
• nonn

Comments

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.

Links

• 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.

Crossrefs

Cf. A079254, A079257, A079258, A080760.

Programs

PARI

{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))}