A302388 a(n) is the least positive integer not yet in the sequence in which the largest digit of a(n-3) appears among its digits; a(1)=1, a(2)=2, a(3)=3.

1, 2, 3, 10, 12, 13, 11, 20, 23, 14, 21, 30, 4, 22, 31, 24, 25, 32, 34, 5, 33, 40, 15, 35, 41, 45, 50, 42, 51, 52, 43, 53, 54, 44, 55, 56, 46, 57, 6, 16, 7, 26, 36, 17, 60, 61, 27, 62, 63, 37, 64, 65, 47, 66, 67, 70, 68, 71, 72, 8, 73, 74, 18, 75, 76, 28, 77, 78, 38, 79, 48, 58, 9, 80

Offset

1,2

Comments

The only fixed points are 1,2,3,99.

Starting from a(87)=89, every term must contain a 9.

First differences are bounded by -64 and 71.

Links

Table of n, a(n) for n=1..74.

Example

a(7)=11 since the largest digit of a(4)=10 is 1, and 11 is the least positive integer at n=7 that contains 1.

Mathematica

Nest[Append[#, Block[{k = 4, d}, While[Nand[FreeQ[#[[All, 1]], k], MemberQ[Set[d, IntegerDigits[k]], Max[#[[-3, -1]] ] ] ], k++]; {k, d}]] &, Transpose@ {#, IntegerDigits@ #} &@ Range[3], 71][[All, 1]] (* Michael De Vlieger, Apr 12 2018 *)

Prog

(PARI) firstTerms(m)={my(Seq:list=List([1, 2, 3]), z, cp, r, ok); cp=vector(10, u, u-1); for(i=4, m, z=vecmax(digits(Seq[i-3])); for(t=1, oo, forvec(y=vector(t, u, [1, #cp]), ok=0; for(j=1, t, if(cp[y[j]]==z, ok=1; break)); if(ok, r=fromdigits(vector(t, u, cp[y[u]])); for(w=1, #Seq, if(r==Seq[w], ok=0; break)); if(ok, listput(Seq, r); break(2)))))); return(Seq)} \\ R. J. Cano, Apr 14 2018

Crossrefs

Cf. A286890, A300907.

Sequence in context: A092986 A295577 A325256 * A006092 A015859 A022427

Adjacent sequences: A302385 A302386 A302387 * A302389 A302390 A302391

Keyword

nonn,base

Author

Enrique Navarrete, Apr 06 2018

Status

approved