A202386
Nonpalindromic numbers m such that the difference between the square of m and the square of the reversal of m is itself a perfect square. Numbers ending in 0 are excluded.
Original entry on oeis.org
65, 5625, 6565, 50721, 65065, 71555, 75515, 84295, 541063, 557931, 650065, 650606, 656565, 699796, 809325, 827372, 934065, 2855182, 4637061, 4854634, 5791775, 5883141, 5951693, 6129084, 6500065, 6731076, 6752626, 6791774, 7768827, 8084505, 9349065
Offset: 1
5625 belongs to this sequence because 5625^2 - 5265^2 = 1980^2.
- A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1996, p. 147.
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lst = {}; Do[a = n^2; b = FromDigits[Reverse[IntegerDigits[n]]]^2; If[MatchQ[Sqrt[a - b], _Integer] && ! a == b, AppendTo[lst, n]], {n, 85000}]; Select[lst, ! Mod[#, 10] == 0 &]
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isok(m) = my(r=fromdigits(Vecrev(digits(m)))); (r != m) && (m % 10) && issquare(m^2 - r^2); \\ Michel Marcus, Feb 27 2020
A256515
Nonpalindromic positive integers k such that the absolute value of k^2 - reverse(k)^2 is a square.
Original entry on oeis.org
56, 65, 5265, 5625, 5656, 6565, 12705, 44370, 50721, 51557, 55517, 56056, 59248, 65065, 71555, 75515, 84295, 139755, 273728, 360145, 481610, 523908, 541063, 557931, 560056, 560439, 565656, 606056, 621770, 650065, 650606, 656565, 697996, 699796, 809325, 827372
Offset: 1
The nonpalindromic number 5265 is a term because abs(5265^2 - 5625^2) = 1980^2.
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[n: n in [0..10^6] | Intseq(n) ne Reverse(Intseq(n)) and IsSquare(s) where s is Abs(n^2-Seqint(Reverse(Intseq(n)))^2)]; // Bruno Berselli, Apr 01 2015
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Select[Range[200000], ! PalindromeQ@ # && IntegerQ@ Sqrt@ Abs[#^2 - IntegerReverse[#]^2] &] (* Michael De Vlieger, Mar 02 2022 *)
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from sympy.ntheory.primetest import is_square
def R(n): return int(str(n)[::-1])
def ok(n): Rn = R(n); return n != Rn and is_square(abs(n**2 - Rn**2))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Mar 02 2022
A113798
Numbers k such that k^2 plus the reverse of k is a square.
Original entry on oeis.org
117, 119817, 13101687, 119819817, 13101801687, 119819819817, 11983101689817, 13101801801687, 119819819819817
Offset: 1
117^2 + 711 = 120^2, thus 117 is a term.
A289140
Positive numbers k such that rev(k)^2 + rev(k^2) is a square, where rev(n) = A004086(n) is the digital reverse of n.
Original entry on oeis.org
998586, 3632658, 9985860, 36326580, 74471091, 99664458, 99858600, 363265800, 634826115, 743193501, 744710910, 756335085, 759317343, 996644580, 998586000, 3632658000, 6348261150, 7177621788, 7431935010, 7447109100, 7563350850, 7593173430, 9966445800
Offset: 1
998586 is a term since rev(998586^2) + 685899^2 = 1079100^2.
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rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; Parallelize@ Select[3 Range[4 10^6], IntegerQ@ Sqrt[rev[#^2] + rev[#]^2] &]
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isok(n) = issquare(fromdigits(Vecrev(digits(n)))^2 + fromdigits(Vecrev(digits(n^2)))); \\ Michel Marcus, Jun 29 2017
Showing 1-4 of 4 results.
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