A397674 Numbers k such that k times its decimal digit reversal is a triangular number.

1, 6, 10, 37, 73, 78, 87, 116, 397, 507, 611, 705, 793, 798, 897, 1200, 2100, 3230, 3997, 7993, 7998, 8997, 15290, 15960, 27930, 29600, 38517, 39720, 39997, 69200, 69510, 71583, 79993, 79998, 89997, 92510, 133640, 175868, 222740, 290170, 399997, 416024, 420614

Offset

1,2

Comments

This sequence is the preimage of A000217 under A061205.

For terms not ending in 0, membership is unchanged by replacing k by A004086(k).

If k = c*10^j with j >= 0 and c is not divisible by 10, then k is a term iff 8*c*A004086(c)*10^j + 1 is a square.

Among decimal palindromes, the terms are exactly the palindromic members of A001109.

For m >= 1, (4*10^m - 3)*(8*10^m - 7) = A000217(8*10^m - 7), so both 4*10^m - 3 and 8*10^m - 7 are terms.

For m >= 1, (8*10^m - 2)*(9*10^m - 3) = A000217(12*10^m - 4), so both 8*10^m - 2 and 9*10^m - 3 are terms.

Links

Geazi Souza Oliveira, Table of n, a(n) for n = 1..84

Example

37*73 = 2701 = A000217(73), so 37 and 73 are terms.
78*87 = 6786 = A000217(116), so 78 and 87 are terms.

Prog

(PARI) isok(k) = ispolygonal(k*fromdigits(Vecrev(digits(k))), 3);
(Python)
from math import isqrt
def isok(n):
    s = 8*n*int(str(n)[::-1]) + 1
    return isqrt(s)**2 == s

Crossrefs

Cf. A000217, A001109, A004086, A061205, A083818, A169830.

Sequence in context: A332984 A038264 A094890 * A213477 A047178 A132095

Adjacent sequences: A397669 A397670 A397671 * A397680 A397681 A397682

Keyword

base,nonn,new

Author

Geazi Souza Oliveira, Jul 04 2026

Status

approved