A065654
Fixed points for A065652, a permutation of the natural numbers.
Original entry on oeis.org
0, 1, 2, 4, 8, 24, 80, 784, 8288, 1053024, 115519040, 2186083514944, 26210587691915648, 9556921325803348132669824, 1373760651292040932579353684066560, 182669489453303120238622839813317479832750842872064
Offset: 0
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f[n_] := f[n] = If[n < 2, n, f[n - 2]^2 + 2]; a[n_] := (f[n] + f[n + 1] - 1)/2; Array[a, 15, 0] (* Amiram Eldar, Mar 19 2025 *)
A065653
a(0) = 0, a(1) = 1, a(n) = a(n-2)*a(n-2) + 2 for n > 1.
Original entry on oeis.org
0, 1, 2, 3, 6, 11, 38, 123, 1446, 15131, 2090918, 228947163, 4371938082726, 52416803445748571, 19113842599189892819591078, 2747521283470239265968814548542043, 365338978906606237729724396156395693696687137202086
Offset: 0
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RecurrenceTable[{a[0]==0,a[1]==1,a[n]==a[n-2]^2+2},a,{n,20}] (* Harvey P. Dale, Aug 19 2013 *)
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a(n)=if(n<2, n>0, 2+a(n-2)^2) /* Michael Somos, Mar 25 2006 */
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{ for (n=0, 24, if (n>1, a=a2^2 + 2; a2=a1; a1=a, if (n, a=a1=1, a=a2=0)); write("b065653.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 25 2009
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