A366197 Lexicographically earliest permutation of the nonnegative integers such that the absolute difference between the digitsum of a(n) and the digitsum of a(n+2) = 1.

0, 1, 10, 2, 11, 3, 12, 4, 13, 5, 14, 6, 15, 7, 16, 8, 17, 9, 18, 19, 26, 27, 25, 28, 24, 29, 23, 37, 22, 36, 21, 35, 20, 34, 30, 33, 31, 32, 41, 40, 42, 50, 43, 51, 44, 52, 45, 53, 46, 54, 38, 55, 39, 47, 49, 48, 57, 56, 58, 64, 59, 63, 67, 62, 66, 61, 65, 60

Offset: 0

Author

Eric Angelini, Oct 03 2023

Keywords

• base
• nonn

Examples

			DS stands hereunder for DigitSum:
a(0) =  0 (DS 0) and a(2) = 10 (DS 1) and the absolute difference 0 - 1 = 1;
a(1) =  1 (DS 1) and a(3) =  2 (DS 2) and the absolute difference 1 - 2 = 1;
a(2) = 10 (DS 1) and a(4) = 11 (DS 2) and the absolute difference 1 - 2 = 1;
a(3) =  2 (DS 2) and a(5) =  3 (DS 3) and the absolute difference 2 - 3 = 1;
a(4) = 11 (DS 2) and a(6) = 12 (DS 3) and the absolute difference 2 - 3 = 1; etc.
		

Links

• John Tyler Rascoe, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A007953, A108971, A318486.

Programs

Python

from itertools import count, filterfalse
def DS(y):
    z = str(y)
    return sum(int(z[i]) for i in range (0,len(z)))
def A366197_list(n_max):
    A = [0,1]
    S = set(A)
    for n in range(2,n_max+1):
        for i in filterfalse(S._contains_, count(1)):
            if abs(DS(A[n-2])-DS(i)) == 1:
                A.append(i)
                S.add(i)
                break
    return(A) # John Tyler Rascoe, Oct 22 2023

Extensions

More terms from Alois P. Heinz, Oct 03 2023