A181789 Pandigital biperiod squares: pandigital squares whose digits repeat twice in order.

183673469387755102041183673469387755102041, 326530612244897959184326530612244897959184, 734693877551020408164734693877551020408164, 132231404958677685950413223140496132231404958677685950413223140496

Offset

1,1

Comments

Ondrejka asks in Problem 1130(b) (see reference) what the smallest biperiod square is in which the ten decimal digits occur equally often (an equipandigital biperiod square), but it remains unknown whether any such square even exists.

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

Prog

(Python)
from itertools import count, islice
from sympy import sqrt_mod
def A181789_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 <= (m:=k**2) < a*(a-1) and len(set(str(m//a))) == 10:
                    yield m
A181789_list = list(islice(A181789_gen(), 20)) # Chai Wah Wu, Mar 23 2024

Crossrefs

Cf. A092118 (biperiod squares), A181790, A181791.

Sequence in context: A095476 A292856 A292846 * A095478 A291353 A095480

Adjacent sequences: A181786 A181787 A181788 * A181790 A181791 A181792

Keyword

nonn,base

Author

William Rex Marshall, Nov 12 2010

Status

approved