A327723 a(1) = 0. For n > 1, a(n) is the smallest positive integer k not already in the sequence such that the least significant digit of k equals the most significant digit of a(n-1).

0, 10, 1, 11, 21, 2, 12, 31, 3, 13, 41, 4, 14, 51, 5, 15, 61, 6, 16, 71, 7, 17, 81, 8, 18, 91, 9, 19, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 201, 22, 32, 23, 42, 24, 52, 25, 62, 26, 72, 27, 82, 28, 92, 29, 102, 211, 112, 221, 122, 231, 132, 241, 142

Offset: 1

Author

Felix Fröhlich, Sep 24 2019

Keywords

• nonn
• base
• easy

Comments

Except for 0 and 10, there are no multiples of 10 (terms of A008592) in the sequence, i.e., any term of the sequence except 0 or 10 is a term of A067251.

Are there any numbers except multiples of 10 that do not occur in the sequence? In other words, is this a permutation of A067251 UNION [0, 10]?

Crossrefs

Cf. A000030, A008592, A010879, A067251.

Programs

Mathematica

L={0}; Do[k = IntegerDigits[ Last@ L][[1]]; While[ MemberQ[L,k], k+=10]; AppendTo[ L, k], {80}]; L (* Giovanni Resta, Sep 24 2019 *)

PARI

isinv(vec, k) = for(t=1, #vec, if(vec[t]==k, return(1))); 0
isvalid(x, y) = my(d=digits(x), e=digits(y)); d[#d]==e[1]
terms(n) = my(v=[0, 10]); while(1, if(#v >= n, return(v)); for(k=1, oo, if(isvalid(k, v[#v]) && !isinv(v, k), v=concat(v, [k]); break)))
terms(100) \\ Print initial 100 terms

Python

n, a, msdc = 0, 0, [1,0,0,0,0,0,0,0,0,0]
while n <= 62:
    print(n,a)
    s = str(a)
    msd = int(s[0])
    n, a = n+1, msdc[msd]*10+msd
    msdc[msd] = msdc[msd]+1 # A.H.M. Smeets, Sep 25 2019

Formula

A010879(a(n)) = A000030(a(n-1)).