A397674 - OEIS

%I #18 Jul 09 2026 07:55:09

%S 1,6,10,37,73,78,87,116,397,507,611,705,793,798,897,1200,2100,3230,

%T 3997,7993,7998,8997,15290,15960,27930,29600,38517,39720,39997,69200,

%U 69510,71583,79993,79998,89997,92510,133640,175868,222740,290170,399997,416024,420614

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

%C This sequence is the preimage of A000217 under A061205.

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

%C 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.

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

%C 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.

%C 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.

%H Geazi Souza Oliveira, <a href="/A397674/b397674.txt">Table of n, a(n) for n = 1..84</a>

%e 37*73 = 2701 = A000217(73), so 37 and 73 are terms.

%e 78*87 = 6786 = A000217(116), so 78 and 87 are terms.

%o (PARI) isok(k) = ispolygonal(k*fromdigits(Vecrev(digits(k))), 3);

%o (Python)

%o from math import isqrt

%o def isok(n):

%o     s = 8*n*int(str(n)[::-1]) + 1

%o     return isqrt(s)**2 == s

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

%K base,nonn,new

%O 1,2

%A _Geazi Souza Oliveira_, Jul 04 2026