Soumil Mandal - cp's OEIS frontend

User: Soumil Mandal

Soumil Mandal has authored 2 sequences.

A270926 Numbers k such that k*R(k) can be represented as the sum of two nonzero squares, where R(k) is the reverse of the decimal expansion of k.

5, 10, 15, 16, 18, 20, 25, 30, 37, 40, 50, 51, 52, 55, 58, 60, 61, 70, 73, 78, 80, 81, 85, 87, 89, 90, 98, 100, 101, 104, 106, 109, 110, 111, 122, 125, 128, 145, 146, 148, 149, 150, 159, 160, 162, 164, 165, 168, 169, 174, 176, 180, 181, 192, 195, 198, 200, 202, 208, 212, 220, 221, 222

Offset: 1

Soumil Mandal, Mar 26 2016

k*R(k) is the square of the hypotenuse of a right triangle.

Palindromes in this sequence are 5, 55, 101, 111, 181, 202, 212, 222, 232, 272, 292, 303, 313, 323, 333, 353, 373, ... - Altug Alkan, Mar 26 2016

			For k=5, R(k)=5 and k*R(k)=25, which is 3^2 + 4^2.
For k=10, R(k)=1 and k*R(k)=10, which is 1^2 + 3^2.
For k=58, R(k)=85 and k*R(k)=4930, which is 13^2 + 69^2.

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Cf. A000404, A004086, A061205.

Select[Range@ 222, Length[PowersRepresentations[# FromDigits@ Reverse@ IntegerDigits@ #, 2, 2] /. {0, } -> Nothing] > 0 &] (* _Michael De Vlieger, Mar 26 2016 *)
stnzsQ[{a_,b_}]:=AllTrue[{a,b},IntegerQ[Sqrt[#]]&]; Select[Range[ 250], Length[ Select[IntegerPartitions[#  IntegerReverse[#],{2}],stnzsQ]] >0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 12 2020 *)

isA000404(n) = {for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))}
lista(nn) = for(n=1, nn, if(isA000404(n*eval(concat(Vecrev(Str(n))))), print1(n, ", "))); \\ Altug Alkan, Mar 26 2016

# Soumil Mandal, Mar 27 2016
def isHypotenuse(num):
    a, b = 1, 1
    a2, b2 = a**2, b**2
    while a2 + b2 <= num:
        while a2 + b2 <= num:
            if a2 + b2 == num:
                return True
            b += 1
            b2 = b**2
        a += 1
        a2 = a**2
        b = 1
        b2 = b**2
    return False
for x in range(20000):
    if isHypotenuse(x * int(str(x)[::-1])):
        print(x)

More terms from Altug Alkan, Mar 26 2016

A270343 Numbers k that end with ( sum of digits of k )^2.

Original entry on oeis.org

0, 1, 81, 3144, 3256, 6225, 6484, 6576, 7121, 7529, 7676, 9100, 9324, 9361, 9729, 9784, 12144, 12256, 15225, 15484, 15576, 16121, 16529, 16676, 18100, 18324, 18361, 18729, 18784, 21144, 21256, 24225, 24484, 24576, 25121

Offset: 1

Soumil Mandal, Mar 15 2016

All terms end with a digit from the set S = {0,1,4,5,6,9}.

The sum of the digits of the numbers repeat and also change with regular intervals. For example, the sum of the digits S1 = {12,16,15,22,24,11,23,26,10,18,19,27,28} which is followed by 3144 to 8784, 12144 to 18784, 21144 to 27784, 30144 to 36784. Again S2 = {21,25,15,22,24,11,23,26,10,18,19,27,28} is followed by 39441 to 45784, 48441 to 54784, 57441 to 67784, 66441 to 72784. It can be seen that a set containing 13 elements repeats itself for 4 consecutive ranges.

			For k=3256, sum of digits is 16 and 16^2 is 256.
For k=7121, sum of digits is 11 and 11^2 is 121.
For k=18784, sum of digits is 22 and 22^2 is 484.

Paolo P. Lava, Table of n, a(n) for n = 1..10000
Soumil Mandal, Graph Of Sum Of Digits
Soumil Mandal, Graph Of Cumulative Sums

Cf. A003226, A008851, A018247, A118881.

Select[Range[0, 20000], Function[n, Function[k, If[n >= k, FromDigits@ Take[#, -IntegerLength@ k] == k, False]][Total[#]^2] &@ IntegerDigits@ n]] (* Michael De Vlieger, Mar 15 2016 *)
esdQ[n_]:=Module[{idn=IntegerDigits[n],idn2=IntegerDigits[ Total[ IntegerDigits[ n]]^2]},Take[ idn,-Length[idn2]]==idn2]; Select[ Range[ 0,26000],esdQ]//Quiet (* Harvey P. Dale, Jan 01 2022 *)

isok(n) = {sds = sumdigits(n)^2; nbs = #Str(sds); ((n - sds) % 10^nbs) == 0;} \\ Michel Marcus, Mar 16 2016

for i in range(0,200000):
    res = pow((sum(map(int,str(i)))),2)
    if(i%pow(10,len(str(res)))==res):print(i)
# Soumil Mandal, Mar 17 2016

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User: Soumil Mandal

A270926 Numbers k such that k*R(k) can be represented as the sum of two nonzero squares, where R(k) is the reverse of the decimal expansion of k.

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