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A092875 Aronson transform of the "evil" sequence (A001969). 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 23 16:48 EST 2020. Contains 331173 sequences. (Running on oeis4.)