A347335 Lexicographically earliest sequence of distinct nonnegative integers such that the sum of three consecutive terms is a palindrome in base 10.

0, 1, 2, 3, 4, 15, 14, 26, 37, 25, 39, 13, 36, 6, 24, 47, 17, 35, 49, 27, 12, 5, 16, 23, 38, 40, 10, 51, 50, 20, 7, 28, 9, 18, 61, 22, 48, 29, 11, 59, 31, 21, 69, 41, 71, 19, 81, 91, 30, 60, 101, 111, 70, 122, 80, 90, 32, 100, 110, 42, 120, 130, 53, 8, 141, 63, 58, 121, 33, 68, 131, 43

Offset: 1

Author

Eric Angelini and Carole Dubois, Aug 28 2021

Keywords

• base
• nonn

Examples

			a(1) + a(2) + a(3) = 0 + 1 + 2 = 3 (palindrome);
a(2) + a(3) + a(4) = 1 + 2 + 3 = 6 (palindrome);
a(3) + a(4) + a(5) = 2 + 3 + 4 = 9 (palindrome);
a(4) + a(5) + a(6) = 3 + 4 + 15 = 22 (palindrome); etc.
		

Crossrefs

Cf. A228730.

Programs

Python

def ispal(n): s = str(n); return s == s[::-1]
def aupton(terms):
    alst, seen = [0, 1], {0, 1}
    for n in range(2, terms):
        an, partial_sum = 1, sum(alst[-2:])
        while an in seen or not ispal(partial_sum + an): an += 1
        alst.append(an); seen.add(an)
    return alst
print(aupton(201)) # Michael S. Branicky, Aug 28 2021