A068536
Numbers m such that m^2 + (reversal of m)^2 is a square. (Leading 0's are ignored.)
Original entry on oeis.org
88209, 90288, 125928, 196020, 368280, 829521, 1978020, 2328480, 5513508, 8053155, 19798020, 86531940, 197998020, 554344560, 556326540, 1960396020, 1979998020, 5543944560, 5925169800, 8820988209, 9028890288, 12592925928, 14011538112, 19602196020, 19799998020
Offset: 1
88209^2 + 90288^2 = 126225^2, so 88209 belongs to the sequence.
-
Do[If[IntegerQ[Sqrt[n^2 + FromDigits[Reverse[IntegerDigits[n]]]^2]], Print[n]], {n, 1, 10^6}]
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.
-
[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
-
Select[Range[200000], ! PalindromeQ@ # && IntegerQ@ Sqrt@ Abs[#^2 - IntegerReverse[#]^2] &] (* Michael De Vlieger, Mar 02 2022 *)
-
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.
-
rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; Parallelize@ Select[3 Range[4 10^6], IntegerQ@ Sqrt[rev[#^2] + rev[#]^2] &]
-
isok(n) = issquare(fromdigits(Vecrev(digits(n)))^2 + fromdigits(Vecrev(digits(n^2)))); \\ Michel Marcus, Jun 29 2017
A332850
Numbers k = a^2 + b^2 such that reversal(k) = a^2 - b^2 for a > b > 0, where reversal is A004086.
Original entry on oeis.org
699796, 4854634, 6752626, 84036010, 931910661, 21584860960, 52554850525, 467170024564, 637843128736, 638730439636, 638734039636, 638943127636, 727830438745, 727834038745, 746710459825, 746754019825, 748943127625, 9894192267061, 401309596403104, 844181015028970
Offset: 1
699796 = 836^2 + 30^2 and 697996 = 836^2 - 30^2.
-
Do[If[IntegerReverse[a^2+b^2]==a^2-b^2,Print[{a^2+b^2,a,b}]],{a,1,50000},{b,1,a-1}]
-
isok(k) = {my(r = fromdigits(Vecrev(digits(k))), s = r+k, d = k-r); d && !(s % 2) && issquare(s/2) && !(d % 2) && issquare(d/2); } \\ Michel Marcus, Feb 27 2020
Showing 1-5 of 5 results.
Comments