A062388 -id:A062388 - cp's OEIS frontend

A082743 a(0)=1, a(1)=2; for n >= 2, a(n) is smallest palindrome greater than 1 which is congruent to 1 (mod n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 55, 11, 111, 121, 66, 99, 121, 33, 171, 55, 77, 101, 22, 111, 323, 121, 101, 131, 55, 141, 88, 121, 373, 33, 232, 171, 141, 181, 1111, 77, 313, 121, 575, 505, 44, 353, 181, 323, 424, 1441, 99, 101, 868, 313, 10601, 55, 111, 393, 343, 929, 414

Offset: 0

Amarnath Murthy, Apr 15 2003

Cf. A082744, A062388, A077528.

f[n_] := Block[{k = 2}, While[ FromDigits[ Reverse[ IntegerDigits[k]]] != k || Mod[k, n] != 1, k++ ]; k]; Table[ f[n], {n, 2, 60}]

a(n) = A077528(n) for n >= 2. - Georg Fischer, Oct 06 2018

Edited and extended by Robert G. Wilson v, Apr 19 2003

A070244 Largest palindrome using minimum number of digits with a digit sum = n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 55, 515, 66, 616, 77, 717, 88, 818, 99, 919, 929, 939, 949, 959, 969, 979, 989, 999, 9559, 95159, 9669, 96169, 9779, 97179, 9889, 98189, 9999, 99199, 99299, 99399, 99499, 99599, 99699, 99799, 99899, 99999

Offset: 0

Amarnath Murthy, May 05 2002

No palindrome with lesser number of digits is possible.

All the palindromes using same (minimum) number of digits are smaller than a(n).

Cf. A062388.

a(0)=0 prepended by Michel Marcus, Aug 20 2015

A213341 Smallest palindrome with digital root n and n + 1 decimal digits.

Original entry on oeis.org

0, 55, 686, 6996, 79897, 799997, 8998998, 89999998, 999989999, 9999999999

Offset: 0

Alexander R. Povolotsky, Jun 09 2012

Formula a(n) = (44/9*(10^n-1)+(10^n+1)*n) gives for n=0 ... 5 another sequence of palindromic terms a(0) = 0, a(1) = 55, a(2) = 686, a(3) = 7887, a(4) = 88888, a(5) = 988889 (which do not fully comply with the definition "smallest palindrome with digital root n and n+1 decimal digits" - because for n = 3, 4, 5 the terms are not the smallest ones possible).

			a(1) = 55 because there is no smaller two digit palindrome with a digital root of 1.

Subsequence of A062388.

A354480 a(n) is the smallest decimal palindrome with Hamming weight n (i.e., with exactly n 1's when written in binary).

Original entry on oeis.org

0, 1, 3, 7, 77, 55, 111, 191, 383, 767, 5115, 11711, 15351, 30703, 81918, 97279, 744447, 978879, 1570751, 3665663, 8387838, 66911966, 66322366, 132111231, 199212991, 389545983, 939474939, 3204444023, 3220660223, 11542724511, 34258485243, 33788788733, 34292629243

Offset: 0

Ilya Gutkovskiy, Jun 02 2022

Cf. A000120, A000225, A002113, A061712, A062388, A089226, A089998, A089999, A102029, A114477.

from itertools import count, islice, product
def pals(startd=1): # generator for base-10 palindromes
    for d in count(startd):
        for p in product("0123456789", repeat=d//2):
            if d//2 > 0 and p[0] == "0": continue
            left = "".join(p); right = left[::-1]
            for mid in [[""], "0123456789"][d%2]:
                yield int(left + mid + right)
def a(n):
    for p in pals(startd=len(str(2**n-1))):
        if bin(p).count("1") == n:
            return p
print([a(n) for n in range(33)]) # Michael S. Branicky, Jun 02 2022

a(21)-a(32) from Michael S. Branicky, Jun 02 2022

cp's OEIS Frontend

A082743 a(0)=1, a(1)=2; for n >= 2, a(n) is smallest palindrome greater than 1 which is congruent to 1 (mod n).

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A070244 Largest palindrome using minimum number of digits with a digit sum = n.

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A213341 Smallest palindrome with digital root n and n + 1 decimal digits.

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A354480 a(n) is the smallest decimal palindrome with Hamming weight n (i.e., with exactly n 1's when written in binary).

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