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

1,1

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

Table of n, a(n) for n=1..69.

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.

Prog

(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))}

Crossrefs

Cf. A079254, A079257, A079258, A080760.

Sequence in context: A331232 A219050 A036049 * A155498 A069149 A042996

Adjacent sequences: A092872 A092873 A092874 * A092876 A092877 A092878

Keyword

easy,nonn

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Status

approved