cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A359346 Reversible pandigital square numbers.

This page as a plain text file.
%I A359346 #20 Jan 23 2023 13:13:09
%S A359346 1234549876609,9066789454321,123452587690084,123454387666009,
%T A359346 123454987660900,123456987654400,123458987664100,123478988652100,
%U A359346 125688987432100,146678985432100,445678965432100,480096785254321,900666783454321,906678945432100,10223418547690084
%N A359346 Reversible pandigital square numbers.
%C A359346 These are perfect squares containing each digit from 0 to 9 at least once and still remain square numbers (not necessarily of the same length) when reversing the digits.
%C A359346 In 1905, inspired by a question about all pandigital square numbers containing each digit from 0 to 9 exactly once (cf. A036745, A156977), the British mathematician Allan Cunningham (1842-1928) asked for reversible and palindromic pandigital square numbers. In his answer, he gives possible solutions, but actually not the least possible numbers he was asking for in his question.
%H A359346 Martin Renner, <a href="/A359346/b359346.txt">Table of n, a(n) for n = 1..458</a>
%H A359346 Allan Cunningham, <a href="https://archive.org/details/educationaltimes58educ/page/273/mode/1up?view=theater">Question 15789</a>, The Educational Times, and Journal of the College of Preceptors 58 (1905), nr. 530 (June 1), p. 273; <a href="https://archive.org/details/educationaltimes59educ/page/39/mode/1up?view=theater">Solution 15789</a>, Ibid., 59 (1906), nr. 537 (Jan. 1), p. 39.
%e A359346 Sequence starts with 1111103^2 = 1234549876609 <~> 9066789454321 = 3011111^2, which is the smallest possible such number.
%o A359346 (Python)
%o A359346 from math import isqrt
%o A359346 from itertools import count, islice
%o A359346 def c(n): return len(set(s:=str(n)))==10 and isqrt(r:=int(s[::-1]))**2==r
%o A359346 def agen(): yield from (k*k for k in count(10**6) if c(k*k))
%o A359346 print(list(islice(agen(), 15))) # _Michael S. Branicky_, Dec 27 2022
%o A359346 (PARI) isok(k) = if (issquare(k), my(d=digits(k)); (#Set(d) == 10) && issquare(fromdigits(Vecrev(d)));); \\ _Michel Marcus_, Dec 31 2022
%Y A359346 Cf. A036745, A061457, A156977, A225218, A359347.
%K A359346 nonn,base
%O A359346 1,1
%A A359346 _Martin Renner_, Dec 27 2022