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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

(list; graph; refs; listen; history; text; internal format)

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