OFFSET
1,1
REFERENCES
Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations, Experimental Math, 28 (2019), 428-439.
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
Author?, MMB message board "big square"
Dr Barker, Can Numbers Like These Be Square?, YouTube video, 2023.
Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations, preprint arXiv:1707.03894 [math.NT], July 14 2017.
MAPLE
f:=proc(n) local i, j, k; i:=cat(n, n); j:=convert(i, decimal, 10); issqr(j); end;
with(numtheory): Digits:=50:for d from 1 to 22 do tendp1:=10^d+1: tendp1fact:=ifactors(tendp1)[2]: n:=mul(piecewise(tendp1fact[i][2] mod 2=1, tendp1fact[i][1], 1), i=1..nops(tendp1fact)):for i from ceil(sqrt((10^(d-1))/n)) to floor(sqrt((10^d-1)/n)) do printf("%d, ", tendp1*n*i^2) od: od: # C. Ronaldo
PROG
(Python)
from itertools import count, islice
from sympy import sqrt_mod
def A092118_gen(): # generator of terms
for j in count(0):
b = 10**j
a = b*10+1
ab, aa = a*b, a*(a-1)
for k in sorted(sqrt_mod(0, a, all_roots=True)):
if ab <= (m:=k**2) < aa:
yield m
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Michael Mark, Dec 15 2004
EXTENSIONS
Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 15 2005
Definition corrected and improved, reference and cross-reference added by William Rex Marshall, Nov 12 2010
Keyword base added by William Rex Marshall, Nov 12 2010
STATUS
approved