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a(1) = 2; for n>1, a(n) = product of digits of (a(n-1)^2).

0

`%I #19 Aug 23 2017 14:35:14
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`%S 2,4,6,18,24,210,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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`%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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`%U 0,0,0,0,0,0
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`%N a(1) = 2; for n>1, a(n) = product of digits of (a(n-1)^2).
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`%e 6 is in the sequence because 4^2=16 and 6*1=6.
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`%e 18 is in the sequence because 6^2=36 and 3*6=18.
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`%e Other similar sequences, starting from 3, 5 and 7, respectively:
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`%e . 3, 9, 8, 24, 210, 0 (0 continued);
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`%e . 5, 10, 0;
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`%e . 7, 36, 108, 144, 0.
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`%t a[1] = 2; a[n_] := a[n] = Times @@ IntegerDigits[a[n - 1]^2]; Array[a, 100] (* _Jean-François Alcover_, May 29 2014 *)
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`%t NestList[Times@@IntegerDigits[#^2]&,2,80] (* _Harvey P. Dale_, Aug 23 2017 *)
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`%Y Cf. A163522.
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`%K nonn,base,easy
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`%O 1,1
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`%A _Vincenzo Librandi_, May 29 2014
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