A181790 Numbers k such that k concatenated with itself is a pandigital biperiod square.

183673469387755102041, 326530612244897959184, 734693877551020408164, 132231404958677685950413223140496, 206611570247933884297520661157025, 297520661157024793388429752066116, 404958677685950413223140495867769

Offset: 1

Author

William Rex Marshall, Nov 12 2010

Keywords

• nonn
• base

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

Crossrefs

Cf. A102567, A181789, A181791.

Programs

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