A347336 Lexicographically earliest sequence of distinct positive integers such that the concatenation of a(n) and a(n+1) added to a(n+2) is a palindrome in base 10.

1, 2, 10, 12, 99, 32, 67, 66, 120, 46, 75, 209, 48, 64, 20, 26, 86, 196, 72, 19, 8, 4, 15, 9, 22, 7, 5, 13, 42, 319, 105, 808, 793, 1115, 282, 829, 553, 375, 1080, 493, 308, 1186, 617, 194, 522, 1069, 156, 445, 206, 338, 264, 569, 993, 82, 17, 11, 60, 61, 55, 71, 94, 33, 16, 127, 34, 87

Offset: 1

Author

Eric Angelini and Carole Dubois, Aug 28 2021

Keywords

• base
• nonn

Examples

			[a(1), a(2)] + a(3) = [1, 2] + 10 = 12 + 10 = 22 (palindrome);
[a(2), a(3)] + a(4) = [2, 10] + 12 = 210 + 12 = 222 (palindrome);
[a(3), a(4)] + a(5) = [10, 12] + 99 = 1012 + 99 = 1111 (palindrome);
[a(4), a(5)] + a(6) = [12, 99] + 32 = 1299 + 32 = 1331 (palindrome); etc.
		

Crossrefs

Cf. A002113, A082216, A347335.

Programs

Python

def ispal(n): s = str(n); return s == s[::-1]
def aupton(terms):
    alst, seen = [1, 2], {1, 2}
    for n in range(2, terms):
        an, partial_sum = 1, int(str(alst[-2]) + str(alst[-1]))
        while an in seen or not ispal(partial_sum + an): an += 1
        alst.append(an); seen.add(an)
    return alst
print(aupton(66)) # Michael S. Branicky, Aug 28 2021