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
Examples
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.
Programs
-
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 *) -
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
Comments