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

Author

Gleb Ivanov, Sep 17 2022

Keywords

• base
• nonn

Crossrefs

Cf. A020485, A002113, A262038.

Programs

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

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