A357195 a(n) is the smallest palindrome of the form k*(2*n+k-1)/2 where k is a positive integer.

1, 2, 3, 4, 5, 6, 7, 8, 9, 33, 11, 969, 222, 99, 66, 33, 242, 282, 424, 161, 66, 22, 212, 252, 646, 171, 55, 252, 414, 555, 525, 99, 33, 474, 1001, 111, 5005, 77, 484, 1111, 1881, 414, 808, 44, 606, 141, 404, 303, 99, 101, 555, 444, 333, 222, 55, 171, 484

Offset

1,2

Links

Table of n, a(n) for n=1..57.

Prog

(Python)
pal10 = lambda n: str(n) == str(n)[::-1]
def seq(n):
    k = 1
    while not pal10(k*(2*n+k-1)//2):k+=1
    return k*(2*n+k-1)//2
print([seq(n) for n in range(1, 100)])
(Python)
from itertools import count
def A357195(n): return next(filter(lambda n:(s := str(n))[:(t:=len(s)+1>>1)]==s[:-t-1:-1], (k*((n<<1)+k-1)>>1 for k in count(1)))) # Chai Wah Wu, Oct 29 2022
(PARI) ispal(p) = my(d=digits(p)); d==Vecrev(d);
a(n) = my(k=1); while(!ispal(x=k*(2*n+k-1)/2), k++); x; \\ Michel Marcus, Sep 17 2022

Crossrefs

Cf. A020485, A002113, A262038.

Sequence in context: A004849 A261279 A295638 * A173551 A271534 A072482

Adjacent sequences: A357192 A357193 A357194 * A357196 A357197 A357198

Keyword

base,nonn

Author

Gleb Ivanov, Sep 17 2022

Status

approved