Jupyter with Sagemath

If you have already installed Jupyter on your computer and want to use that with sagemath. You can easily invoke jupyter instead of the ipython notebook of sagemath with the following command that you should type at the sage prompt
sage: !sage -n jupyter
or if you want to launch from the prompt then type
sage -n jupyter 

How many triangular numbers are also Fibonacci Numbers

I heard this from Bruce Edwards that they are only 5 and these are 1,1,3,21, and 55. I wrote a program in Sagemath to verify that. Here it is Here is the program with its output

def fibo(n):
    fib_1 = 1
    fib_2 = 1
    if n == 1 or n== 2:
        return 1
    fib_n=0
   
    for i in range(3,n+1):
        fib_n = fib_1+fib_2
        fib_1 = fib_2
        fib_2 = fib_n
    return fib_n
def triNumList(n):
    a=[]
    for i in range(1,n):
        b=i*(i+1)/2
        a.append(b)
    return a

def fiboList(n):
    a=[]
    for i in range(1,n):
        a.append(fibo(i))
    return a

def TriFiboCompare(n):
    f = fiboList(n)
    t = triNumList(n)
    print(f)
    print(t)
    for i in f:
        if i in t:
            print("Match",i)

TriFiboCompare(100)


[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, 7778742049, 12586269025, 20365011074, 32951280099, 53316291173, 86267571272, 139583862445, 225851433717, 365435296162, 591286729879, 956722026041, 1548008755920, 2504730781961, 4052739537881, 6557470319842, 10610209857723, 17167680177565, 27777890035288, 44945570212853, 72723460248141, 117669030460994, 190392490709135, 308061521170129, 498454011879264, 806515533049393, 1304969544928657, 2111485077978050, 3416454622906707, 5527939700884757, 8944394323791464, 14472334024676221, 23416728348467685, 37889062373143906, 61305790721611591, 99194853094755497, 160500643816367088, 259695496911122585, 420196140727489673, 679891637638612258, 1100087778366101931, 1779979416004714189, 2880067194370816120, 4660046610375530309, 7540113804746346429, 12200160415121876738, 19740274219868223167, 31940434634990099905, 51680708854858323072, 83621143489848422977, 135301852344706746049, 218922995834555169026] [1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, 1485, 1540, 1596, 1653, 1711, 1770, 1830, 1891, 1953, 2016, 2080, 2145, 2211, 2278, 2346, 2415, 2485, 2556, 2628, 2701, 2775, 2850, 2926, 3003, 3081, 3160, 3240, 3321, 3403, 3486, 3570, 3655, 3741, 3828, 3916, 4005, 4095, 4186, 4278, 4371, 4465, 4560, 4656, 4753, 4851, 4950] ('Match', 1) ('Match', 1) ('Match', 3) ('Match', 21) ('Match', 55)