A225301
Number of solutions to rev(x^2) = rev(x)^2 with at most n digits, where the function rev(x) reverses the digits of x.
Original entry on oeis.org
4, 10, 25, 64, 154, 363, 820, 1811, 3873, 8161, 16682, 33757, 66865, 130938, 251983, 480794, 903982, 1685564, 3106009, 5677864, 10276936, 18464659, 32891188, 58169965, 102136773, 178096365, 308593320, 531191385, 909227947, 1546356486, 2617639293
Offset: 1
For n = 2 the a(2) = 10 solutions are 0, 1, 2, 3, 11, 12, 13, 21, 22, 31.
A098690
Number of solutions to rev(x^2)=rev(x)^2 below 10^n.
Original entry on oeis.org
3, 9, 24, 63, 153, 362, 819, 1810, 3872, 8160, 16681, 33756, 66864, 130937, 251982, 480793, 903981, 1685563, 3106008, 5677863, 10276935, 18464658, 32891187, 58169964, 102136772, 178096364, 308593319, 531191384, 909227946, 1546356485, 2617639292
Offset: 1
For n = 2 the a(2) = 9 solutions are 1, 2, 3, 11, 12, 13, 21, 22, 31. - _David Radcliffe_, Aug 28 2021
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f[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Differences[Table[Length[Select[Range[10^n],f[#^2]==f[#]^2&]],{n,0,6}]] (* Geoffrey Critzer, Dec 18 2013 *)
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def rev(n): return int(str(n)[::-1])
def a(n): return sum(k % 10 and rev(k**2) == rev(k)**2 for k in range(10**n)) # David Radcliffe, Aug 28 2021
A340491
Number of n-digit numbers x such that rev(x^2) = rev(x)^2 and x does not contain any zero digits, where rev(x) is the digit reversal of x.
Original entry on oeis.org
3, 6, 9, 11, 10, 7, 7, 1, 1
Offset: 1
The 7 solutions with 7 digits are 1111111, 1111112, 1111121, 1111211, 1121111, 1211111, 2111111.
Cf.
A098701 (number of solutions) and
A085305 (the solutions), where digit 0 is not forbidden.
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isok(k) = my(d=digits(k)); vecmin(d) && (fromdigits(Vecrev(digits(k^2))) == fromdigits(Vecrev(d))^2);
a(n) = sum(k=10^(n-1), 10^n-1, isok(k)); \\ Michel Marcus, Jan 16 2021
Showing 1-3 of 3 results.
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