A303657 a(n) is the least positive integer not yet in the sequence which shares a digit with a(n-2); a(1)=0, a(2)=1.

0, 1, 10, 11, 12, 13, 2, 3, 20, 23, 21, 22, 14, 24, 4, 25, 34, 5, 30, 15, 31, 16, 17, 6, 7, 26, 27, 28, 29, 8, 9, 18, 19, 38, 39, 32, 33, 35, 36, 37, 43, 47, 40, 41, 42, 44, 45, 46, 48, 49, 54, 59, 50, 51, 52, 53, 55, 56, 57, 58, 65, 68, 60, 61, 62, 63, 64, 66

Offset

1,3

Comments

Up to n=34 the first differences of the sequence are bounded by -29 and 25; the bounds are -10 and 10 thereafter.

From a(103)=100 onwards, the sequence has slope = 1 with minor jumps about every 100 terms.

It appears that this sequence has an inverse, namely 1, 2, 7, 8, 15, 18, 24, 25, 30, 31, 3, 4, 5, 6, 13, 20, 22, 23, 32, 33, 9, ..., . - Robert G. Wilson v, Apr 29 2018 [Edited by Rémy Sigrist, May 06 2018]

Links

Table of n, a(n) for n=1..68.

R. J. Cano, Sequencer program in PARI.

Example

a(7)=2 since it is the least positive integer not yet in the sequence which shares a digit with a(5)=12.

Mathematica

f[s_List] := Block[{k = 2, l = Union@ IntegerDigits@ s[[-2]]}, While[MemberQ[s, k] || Intersection[l, IntegerDigits@ k] == {}, k++]; Append[s, k]]; Nest[f, {0, 1}, 70] (* Robert G. Wilson v, Apr 29 2018 *)

Prog

(PARI) Digits(x, b)=if(!x, [0], digits(x, b));
firstTerms(n, {k=2}, {b=10})={my(N=b*n); my(s=List(vector(N, u, u-1)), t, x, y); for(m=k+1, n, x=Set(Digits(s[m-k], b)); for(i=m, N, y=Set(Digits(s[i], b)); if(#setintersect(x, y), t=s[i]; listpop(s, i); listinsert(s, t, m); break))); return(Vec(s)[1..n])}
a(n)=firstTerms(n)[n]; \\ R. J. Cano, May 05 2018
(PARI) See Cano link.

Crossrefs

Cf. A107353, A303605.

Sequence in context: A347180 A123895 A147519 * A342367 A303879 A305947

Adjacent sequences: A303654 A303655 A303656 * A303658 A303659 A303660

Keyword

nonn,base

Author

Enrique Navarrete, Apr 27 2018

Status

approved