A347402 -id:A347402 - cp's OEIS frontend

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

Eric Angelini and Carole Dubois, Aug 30 2021

			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.

Cf. A347335, A347336, A347401, A347402.

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

A347401 Lexicographically earliest sequence of distinct terms > 0 such that the sum n + a(n) forms a palindrome in base 10.

Original entry on oeis.org

1, 2, 3, 4, 6, 5, 15, 14, 13, 12, 11, 10, 9, 8, 7, 17, 16, 26, 25, 24, 23, 22, 21, 20, 19, 18, 28, 27, 37, 36, 35, 34, 33, 32, 31, 30, 29, 39, 38, 48, 47, 46, 45, 44, 43, 42, 41, 40, 50, 49, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 80, 79, 78, 77, 76, 75, 74, 73

Offset: 1

Eric Angelini and Carole Dubois, Aug 30 2021

			For n = 4 we have a(4) = 4 and 4 + 4 = 8 is a palindrome in base 10;
for n = 5 we have a(5) = 6 and 5 + 6 = 11 is a palindrome in base 10;
for n = 6 we have a(6) = 5 and 6 + 5 = 11 is a palindrome in base 10;
for n = 7 we have a(7) = 15 and 7 + 15 = 22 is a palindrome in base 10;
for n = 8 we have a(8) = 14 and 8 + 14 = 22 is a palindrome in base 10; etc.

Cf. A347335, A347336, A347400, A347402.

def ispal(n): s = str(n); 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(n + an): an += 1
        alst.append(an); seen.add(an)
    return alst
print(aupton(200)) # Michael S. Branicky, Aug 30 2021

A376856 a(1) = 1; for n > 1, a(n) is the smallest unused positive number such that a(n), |a(n) - a(n-1)| and a(1) + ... +a(n) are all palindromes.

Original entry on oeis.org

1, 2, 3, 5, 11, 22, 33, 44, 121, 222, 101, 202, 454, 1221, 2222, 1001, 2002, 4554, 12221, 22222, 10001, 20002, 45554, 122221, 222222, 100001, 200002, 455554, 1222221, 2222222, 1000001, 2000002, 4555554, 12222221, 22222222, 10000001, 20000002, 45555554, 122222221, 222222222, 100000001, 200000002, 455555554, 1222222221, 2222222222, 1000000001

Offset: 1

Scott R. Shannon, Oct 06 2024

The sequence is infinite as from a(13) onward a repetitive pattern of five numbers appears, 45...54, 12...21, 22...22, 10...01, 20...02, all of which grow by one extra digit each iteration.

			a(9) = 121 as 121 is a palindrome, |121 - 44| = 77 is a palindrome, and 1 + 2 + 3 + 5 + 11 + 22 + 33 + 44 + 121 = 242 is a palindrome.

Cf. A073880, A073879, A002113, A369127, A361335, A347402.

cp's OEIS Frontend

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

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A347401 Lexicographically earliest sequence of distinct terms > 0 such that the sum n + a(n) forms a palindrome in base 10.

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Author

Keywords

Examples

Crossrefs

Programs

Python

A376856 a(1) = 1; for n > 1, a(n) is the smallest unused positive number such that a(n), |a(n) - a(n-1)| and a(1) + ... +a(n) are all palindromes.

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