A045541 Square previous term and then delete digits of previous term.

2, 4, 16, 25, 6, 3, 9, 81, 656, 43033, 18518989, 3422322, 11718787168, 33299240224, 118856557176, 42330949, 17161, 29449992, 867300880006, 522114591215, 760366360676, 5815244491919, 3370600766306, 11949525822594424885

Offset

0,1

Comments

After 100 steps enters a cycle of length 307: a(n+307)=a(n) for n>100; a(167) = 88703778700083013187738001 is the largest term. - Reinhard Zumkeller, Sep 15 2011

Links

Reinhard Zumkeller and Chai Wah Wu, Table of n, a(n) for n = 0..10000 First 1001 terms from Reinhard Zumkeller.

Index entries for linear recurrences with constant coefficients, order 307.

Example

a(100)^2 = 46629^2 = 2174263641 --> 1731 = a(301);
a(407)^2 = 646^2 = 417316 --> 1731 = a(408) = a(301+307).

Mathematica

nxt[n_]:=Module[{idn=IntegerDigits[n], idn2=IntegerDigits[n^2]}, Table[ idn2= DeleteCases[ idn2, idn[[i]]], {i, Length[idn]}]; FromDigits[idn2]]; NestList[nxt, 2, 30] (* Harvey P. Dale, Oct 29 2011 *)

Prog

(Haskell)
a045541 n = a045541_list !! n
a045541_list = 2 : f 2 where
   f x = x' : f x'
       where x' = read $ filter (`notElem` show x) $ show (x^2)
-- Reinhard Zumkeller, Sep 15 2011
(Python)
A045541_list, l = [2], 2
for _ in range(10**4):
....l = int(''.join(d for d in str(l**2) if not d in set(str(l))))
....A045541_list.append(l) # Chai Wah Wu, Jan 03 2015
(PARI) deldig(n, m)=my(s=Set(digits(m))); fromdigits(select(k->!setsearch(s, k), digits(n)))
a(n)=if(n, my(k=a(n-1)); deldig(k^2, k), 2) \\ Charles R Greathouse IV, Jun 16 2015

Crossrefs

Sequence in context: A059622 A131475 A239363 * A372898 A234639 A358000

Adjacent sequences: A045538 A045539 A045540 * A045542 A045543 A045544

Keyword

base,nonn,nice,look,easy

Author

Erich Friedman

Status

approved