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

Author

Eric Angelini and Hans Havermann, May 27 2023

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Programs

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

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

Extensions

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