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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.
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
0,3
LINKS
EXAMPLE
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.
PROG
(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
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini, Oct 03 2023
EXTENSIONS
More terms from Alois P. Heinz, Oct 03 2023
STATUS
approved