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A045541 Square previous term and then delete digits of previous term. 1
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

(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 * A234639 A275674 A225983

Adjacent sequences:  A045538 A045539 A045540 * A045542 A045543 A045544

KEYWORD

base,nonn,nice,look,easy

AUTHOR

Erich Friedman

STATUS

approved

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Last modified November 22 16:26 EST 2019. Contains 329396 sequences. (Running on oeis4.)