1,1

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 (math.NT/0305308)

(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(n<v[pv], n+=1; while(n==v[pv], n+=1; pv+=1); x=concat (x, n); n+=1; i+=1, while((n<l)&&(v[pv]==n), x=concat (x, n); n+=1; pv+=1; i+=1));

/*The induction:*/ while(abs(pv)<=l&&n<v[l], k=x[i]; n=k; pv=isin(i+1, v, l, pv);

/* pv>0 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&&x<v[1], return(-poi), if(x<v[poi], while(x<v[poi]&&poi>1, poi-=1); if(x<>v [poi], poi*=-1), if(x>v[poi], while(x>v[poi]&&poi<l, poi+=1); if(x<>v [poi], poi*=-1))); return(poi))}

Cf. A079254, A079257, A079258, A080760.

Sequence in context: A133677 A075750 A036049 this_sequence A155498 A069149 A042996

Adjacent sequences: A092872 A092873 A092874 this_sequence A092876 A092877 A092878

easy,nonn

Ferenc Adorjan (fadorjan(AT)freemail.hu)