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

1,2

Links

Table of n, a(n) for n=1..66.

Example

[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.

Prog

(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

Crossrefs

Cf. A002113, A082216, A347335.

Sequence in context: A055697 A055705 A156430 * A303356 A299317 A095914

Adjacent sequences: A347333 A347334 A347335 * A347337 A347338 A347339

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Aug 28 2021

Status

approved