A001042 -id:A001042 - cp's OEIS frontend

A064236 Number of decimal digits in A001042.

1, 1, 1, 1, 2, 3, 5, 10, 19, 38, 76, 152, 303, 605, 1210, 2420, 4839, 9678, 19355, 38709, 77417, 154834, 309667, 619333, 1238665, 2477330, 4954660, 9909319, 19818638, 39637275, 79274549

Offset: 0

Jason Earls, Sep 22 2001

a064236 = length . show . a001042  -- Reinhard Zumkeller, Dec 16 2013

a[ 1 ] = 1; a[ 2 ] = 2; a[ n_ ] := a[ n ] = a[ n - 1 ]^2 - a[ n - 2 ]^2; Table[ Floor[ N[ Log[ 10, a[ n ] ], 36 ] ] + 1, {n, 1, 31} ]
IntegerLength[#]&/@(RecurrenceTable[{a[1]==1,a[2]==2,a[n]==a[n-1]^2- a[n-2]^2},a,{n,31}]) (* Harvey P. Dale, Dec 27 2013 *)

a(n) = if(n<2,n+1,a(n-1)^2-a(n-2)^2); l(n) = ln=0; while(n,n=floor(n/10); ln++); return(ln); for(n=0,21,print(l(a(n))))

More terms from Robert G. Wilson v, Sep 24 2001

A062000 a(n) = a(n-1)^2 - a(n-2)^2 with a(0) = 0, a(1) = 2.

Original entry on oeis.org

0, 2, 4, 12, 128, 16240, 263721216, 69548879504781056, 4837046640370554355727482727956480, 23397020201120067002755280700388456275000098577861376610994277515264

Offset: 0

Henry Bottomley, May 29 2001

nonn

			a(3) = 4^2 - 2^2 = 12.

Harry J. Smith, Table of n, a(n) for n = 0..12
Index entries for sequences of form a(n+1)=a(n)^2 + ...

Cf. A001042 and A057078 have the same recurrence.

Cf. A061999.

t = {0, 2}; Do[AppendTo[t, t[[-2]]^2 - t[[-1]]^2], {n, 8}]; Abs[t] (* Vladimir Joseph Stephan Orlovsky, Feb 23 2012 *)
RecurrenceTable[{a[0]==0, a[1]==2, a[n]==a[n-1]^2 - a[n-2]^2}, a, {n, 0, 10}] (* Vaclav Kotesovec, Dec 17 2014 *)

{ for (n=0, 12, if (n>1, a=a1^2 - a2^2; a2=a1; a1=a, if (n==0, a=a2=0, a=a1=2)); write("b062000.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 29 2009

def a(n): # a = A062000
    if (n<2): return 2*n
    else: return a(n-1)^2 - a(n-2)^2
[a(n) for n in (0..14)] # G. C. Greubel, May 01 2022

a(n) = 2*A061999(n).

a(n) ~ c^(2^n), where c = 1.35388068260888709216374860554901303232201699191445590979673901150215855854... . - Vaclav Kotesovec, Dec 17 2014

First term corrected by Harry J. Smith, Jul 29 2009

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A064236 Number of decimal digits in A001042.

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A062000 a(n) = a(n-1)^2 - a(n-2)^2 with a(0) = 0, a(1) = 2.

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