OFFSET
1,1
COMMENTS
f(x) = digsum(x)^2 + 1 < x for x >= 400, and all iterations terminate in a single digit or lead to the cycle 65 -> 122 -> 26. - Michael S. Branicky, May 14 2021
EXAMPLE
11 is in the list because (1+1)^2 + 1 = 5.
12 is not in the list because repeatedly iterating the function starting with f(1) = 12 will yield 2 before 5.
13 is not in the list because it will never yield 5. Specifically, 13 -> 17 -> 65 -> 122 -> 26 -> 65 -> ... .
MATHEMATICA
Select[Range@100, Last@NestWhileList[Total[IntegerDigits@#]^2+1&, #, #>10&&#!=26&]==5&] (* Giorgos Kalogeropoulos, May 12 2021 *)
PROG
(Python)
def f(n):
s = 0
while n > 0:
s, n = s+n%10, n//10
return s*s+1
n, pota = 0, 0
while n < 62:
a, repf, i, ii = pota, 0, 0, 4
while a > 9 and a != repf:
a, i = f(a), i+1
if i == ii:
repf, ii = a, 2*ii
if a == 5:
n = n+1
print(pota, end = ", ")
pota = pota+1 # A.H.M. Smeets, May 13 2021
(Python)
def f(x): return sum(map(int, str(x)))**2 + 1
def ok(n):
iter = n # set to f(n) if number of iterations must be >= 1
while iter > 9:
if iter in {65, 122, 26}: return False
iter = f(iter)
return iter == 5
print(list(filter(ok, range(1, 155)))) # Michael S. Branicky, May 19 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Joseph Brown, May 11 2021
STATUS
approved