A268449 Last digit of a(n) + first digit of a(n+1) occurs as a substring in a(n); lexicographic first sequence with this property and no duplicates.

10, 100, 101, 90, 91, 80, 81, 70, 71, 60, 61, 50, 51, 40, 41, 30, 31, 20, 21, 102, 82, 62, 42, 200, 201, 103, 72, 52, 32, 104, 63, 300, 301, 210, 105, 53, 211, 106, 43, 107, 302, 108, 220, 221, 109, 110, 112, 92, 73, 400, 401, 310, 113, 83, 54, 114, 74, 311

Offset

1,1

Comments

A permutation of the numbers of the form 10k+z, 0 <= z <= 9, k having a digit > z or a digit 1 followed by a digit < z.

Sequence suggested by Eric Angelini, first 500 terms independently computed by Jack Brennen, cf. link to SeqFan list.

Links

M. F. Hasler, Table of n, a(n) for n = 1..10000

E. Angelini, A sum visible in the 1st integer, and replies to this post, SeqFan list, Feb. 4, 2016.

Prog

(PARI) EA(n, a=List(10), u=[0])={ my(isok(n)=vecmax(n=digits(n))>n[#n] || sum(i=1, #n-2, n[i]==1 && n[i+1]<n[#n])); for(n=1, n-1, u=setunion(u, [a[n]]); until( isok(u[1]+1) || !u[1]++ , while(#u>1&&u[2]==u[1]+1, u=u[^1])); ok=setintersect(apply(t->t-a[n]%10, Set(concat(ok=digits(a[n]), vector(#ok-1, i, ok[i+1]+ok[i]*10)))), [1..9]); for(k=u[1]+1, 9e9, setsearch(u, k) && next; isok(k) || next; setsearch(ok, digits(k)[1]) && listput(a, k) && break; k=digits(k); k=(k[1]+1)*10^(#k-1)-1)); Vec(a)}

Crossrefs

Cf. A267759 (admissible numbers; range of this sequence).

Cf. A267760, A267761, A267762, A267771, A267772.

Sequence in context: A316915 A352575 A266798 * A289826 A309390 A341692

Adjacent sequences: A268446 A268447 A268448 * A268450 A268451 A268452

Keyword

nonn,base,look

Author

M. F. Hasler, Feb 04 2016

Status

approved