This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
75 -> 7^5 = 16807 -> 1^6*8^0*7 = 7.
33 -> 3^3 = 27 -> 2^7 = 128 -> 1^2*8 = 8.
25 -> 2^5 = 32 -> 3^2 = 9.
def powertrain(n):
p, s = 1, str(n)
if len(s)%2 == 1: s += '1'
for b, e in zip(s[0::2], s[1::2]): p *= int(b)**int(e)
return p
def aupto(limit, target=0):
alst = []
for n in range(1, limit+1):
m, ptm = n, powertrain(n)
while m != ptm: m, ptm = ptm, powertrain(ptm)
if m == target: alst.append(n)
return alst
print(aupto(1191, target=9)) # Michael S. Branicky, Sep 25 2021
Under the powerback map of A133048, 25 -> 5^2 = 25, 107495424 -> 4^2*4^5*9^4*7^0*1 = 107495424.
86 is in the sequence because 8*6 = 48, 4*8 = 32 and 3*2 = 6. And 86 = 48 + 32 + 6.
fQ[n_] := Block[{i = Ceiling[IntegerLength[n]/2], g}, g[x_] := If[IntegerLength@ x <= i, x, Times @@ (FromDigits /@ {If[IntegerLength@ x - i == 0, Nothing, Take[IntegerDigits@ x, IntegerLength@ x - i]], Take[IntegerDigits@ x, -i]})]; Total@ Rest@ Most@ FixedPointList[g, n] == n]; Select[Range@ 500000, fQ] (* Michael De Vlieger, Nov 06 2015 *)
def pod(n, m):
kk = 1
while n > 0:
kk= kk*(n%m)
n =int(n//m)
return kk
for b in range(0, 6):
dd, bb=0, (b-1)//2+2
j=10**bb
for c in range (10*j, 100*j):
d, a, ca=0, 0, pod(c, j)
while ca>0:
d, a=d+ca, a+1
if ca
Comments