A347400 Lexicographically earliest sequence of distinct terms > 0 such that concatenating n to a(n) forms a palindrome in base 10.

1, 2, 3, 4, 5, 6, 7, 8, 9, 101, 11, 21, 31, 41, 51, 61, 71, 81, 91, 102, 12, 22, 32, 42, 52, 62, 72, 82, 92, 103, 13, 23, 33, 43, 53, 63, 73, 83, 93, 104, 14, 24, 34, 44, 54, 64, 74, 84, 94, 105, 15, 25, 35, 45, 55, 65, 75, 85, 95, 106, 16, 26, 36, 46, 56, 66, 76, 86, 96, 107, 17, 27, 37, 47, 57

Offset

1,2

Links

Table of n, a(n) for n=1..75.

Example

For n = 8 we have a(8) = 8 and 88 is a palindrome in base 10;
for n = 9 we have a(9) = 9 and 99 is a palindrome in base 10;
for n = 10 we have a(10) = 101 and 10101 is a palindrome in base 10;
for n = 11 we have a(11) = 11 and 1111 is a palindrome in base 10;
for n = 12 we have a(12) = 21 and 1221 is a palindrome in base 10; etc.

Prog

(Python)
def ispal(s): return s == s[::-1]
def aupton(terms):
    alst, seen = [1], {1}
    for n in range(2, terms+1):
        an = 1
        while an in seen or not ispal(str(n) + str(an)): an += 1
        alst.append(an); seen.add(an)
    return alst
print(aupton(200)) # Michael S. Branicky, Aug 30 2021

Crossrefs

Cf. A347335, A347336, A347401, A347402.

Sequence in context: A080436 A135295 A122625 * A056544 A082216 A052426

Adjacent sequences: A347397 A347398 A347399 * A347401 A347402 A347403

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Aug 30 2021

Status

approved