A362335 Lexicographically earliest sequence of distinct nonnegative terms wherein every digit of a(n) is the absolute difference of two adjacent digits in a(n+1).

0, 11, 10, 100, 110, 112, 102, 1002, 1022, 1102, 1120, 1124, 1026, 10028, 10086, 10082, 10866, 10822, 10886, 10882, 11086, 11082, 11208, 11976, 10928, 100913, 10096, 10093, 10966, 10933, 10996, 10993, 11096, 11093, 22309, 11309, 23009, 13009, 23099, 13099, 23309

Offset

1,2

Comments

All terms > a(24) contain at least one 9 with an adjacent 0. All terms > a(25) contain at least one instance of identical adjacent digits.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(125) = 9902. The next term is 10097, not 20009, because, in spite of its providing more digit differences than are needed, it is lexicographically earlier.

Prog

(Python)
from itertools import count, islice
def c(k, d):
    dk = list(map(int, str(k)))
    return set(abs(dk[i+1]-dk[i]) for i in range(len(dk)-1)) >= d
def agen(): # generator of terms
    an, aset = 0, {0}
    while True:
        yield an
        d = set(map(int, set(str(an))))
        an = next(k for k in count(10**len(d)) if k not in aset and c(k, d))
        aset.add(an)
print(list(islice(agen(), 41))) # Michael S. Branicky, May 27 2023
def A362335(n, A=[0]):
    while len(A) <= n:
        z = lambda a: zip(d := tuple(int(d) for d in str(a)), d[1:])
        D = set(str(A[-1])) ; a = 10**len(D)
        while a in A or D - set(str(abs(x-y)) for x, y in z(a)): a += 1
        A . append(a)
    return A[n] # M. F. Hasler, May 27 2023
(PARI) {upto(N) = my(U=[], a=0); vector(N, n, if(n>1, my(da=Set(if(a, digits(a)))); a=10^#da; while( setsearch(U, a) || #setminus(da, Set(abs((n=digits(a))[^1]-n[^-1]))), a++)); U=setunion(U, [a]); a)} \\ M. F. Hasler, May 27 2023

Crossrefs

Sequence in context: A373693 A275782 A120005 * A105026 A350671 A077326

Adjacent sequences: A362332 A362333 A362334 * A362336 A362337 A362338

Keyword

nonn,base

Author

Eric Angelini and Hans Havermann, May 27 2023

Extensions

a(27) and beyond from Michael S. Branicky, May 27 2023

Status

approved