A177874 The number of decimal digits in the Lucas-Lehmer number A003010(n).

1, 2, 3, 5, 10, 19, 37, 74, 147, 293, 586, 1172, 2343, 4686, 9371, 18742, 37484, 74967, 149933, 299866, 599731, 1199461, 2398922, 4797844, 9595688, 19191376, 38382751, 76765501, 153531001, 307062002, 614124003, 1228248006, 2456496012, 4912992024, 9825984047

Offset: 0

Author

G. L. Honaker, Jr., Dec 13 2010

Keywords

• nonn
• base

Crossrefs

Cf. A003010.

Programs

Magma

T:=[ n eq 1 select 4 else Self(n-1)^2-2: n in [1..24] ]; [ #Intseq(T[n]): n in [1..#T] ];

Mathematica

a=Sqrt[6]; Table[a=a^2-2; Length[IntegerDigits[a]], {n,0,20}]
IntegerLength/@NestList[#^2-2&,4,33] (* Harvey P. Dale, Jan 19 2018 *)

Formula

a(n) = A055642(A003010(n)).

Extensions

a(21)-a(24) from Klaus Brockhaus, Dec 13 2010

a(25)-a(32) from D. S. McNeil, Dec 13 2010

a(33)-a(34) from Jinyuan Wang, Jan 15 2025