A181790 Numbers k such that k concatenated with itself is a pandigital biperiod square.
183673469387755102041, 326530612244897959184, 734693877551020408164, 132231404958677685950413223140496, 206611570247933884297520661157025, 297520661157024793388429752066116, 404958677685950413223140495867769
Offset: 1
References
- 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.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..34
Programs
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Python
from itertools import count, islice from sympy import sqrt_mod def A181790_gen(): # generator of terms for j in count(9): b = 10**j a = b*10+1 for k in sorted(sqrt_mod(0,a,all_roots=True)): if a*b <= k**2 < a*(a-1) and len(set(str(m:=k**2//a))) == 10: yield m A181790_list = list(islice(A181790_gen(),20)) # Chai Wah Wu, Mar 23 2024