A181790 - OEIS

%I #17 Mar 24 2024 10:49:08

%S 183673469387755102041,326530612244897959184,734693877551020408164,

%T 132231404958677685950413223140496,206611570247933884297520661157025,

%U 297520661157024793388429752066116,404958677685950413223140495867769

%N Numbers k such that k concatenated with itself is a pandigital biperiod square.

%D R. Ondrejka, Problem 1130: Biperiod Squares, Journal of Recreational Mathematics, Vol. 14:4 (1981-82), 299. Solution by F. H. Kierstead, Jr., JRM, Vol. 15:4 (1982-83), 311-312.

%H Chai Wah Wu, <a href="/A181790/b181790.txt">Table of n, a(n) for n = 1..34</a>

%o (Python)

%o from itertools import count, islice

%o from sympy import sqrt_mod

%o def A181790_gen(): # generator of terms

%o     for j in count(9):

%o         b = 10**j

%o         a = b*10+1

%o         for k in sorted(sqrt_mod(0,a,all_roots=True)):

%o             if a*b <= k**2 < a*(a-1) and len(set(str(m:=k**2//a))) == 10:

%o                     yield m

%o A181790_list = list(islice(A181790_gen(),20)) # _Chai Wah Wu_, Mar 23 2024

%Y Cf. A102567, A181789, A181791.

%K nonn,base

%O 1,1

%A _William Rex Marshall_, Nov 12 2010