A178094 -id:A178094 - cp's OEIS frontend

A175723 a(1)=a(2)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)), where gpf = "greatest prime factor".

1, 1, 2, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5

Offset: 1

N. J. A. Sloane, Dec 16 2010

nonn

Rapidly enters a loop with period 3,5,2,7.

More generally, if a(1) and a(2) are distinct positive numbers with a(1)+a(2) >= 2, the sequence eventually enters the cycle {7,3,5,2} [Back and Caragiu].

G. Back and M. Caragiu, The greatest prime factor and recurrent sequences, Fib. Q., 48 (2010), 358-362.

Cf. A000045, A006530, A020639.

Similar or related sequences: A177904, A177923, A178094, A178095, A178174, A178179, A180101, A180107, A221183.

nxt[{a_,b_}]:={b,FactorInteger[a+b][[-1,1]]}; Transpose[NestList[nxt,{1,1},120]][[1]] (* or *) PadRight[{1,1,2},130,{5,2,7,3}] (* Harvey P. Dale, Feb 24 2015 *)

A178095 a(1)=a(2)=a(3)=1; thereafter a(n) = lpf(a(n-1)+a(n-2)+a(n-3)), where lpf = "least prime factor".

Original entry on oeis.org

1, 1, 1, 3, 5, 3, 11, 19, 3, 3, 5, 11, 19, 5, 5, 29, 3, 37, 3, 43, 83, 3, 3, 89, 5, 97, 191, 293, 7, 491, 7, 5, 503, 5, 3, 7, 3, 13, 23, 3, 3, 29, 5, 37, 71, 113, 13, 197, 17, 227, 3, 13, 3, 19, 5, 3, 3, 11, 17, 31, 59, 107, 197, 3, 307, 3, 313, 7, 17, 337, 19, 373, 3, 5, 3, 11, 19, 3, 3, 5, 11, 19, 5, 5, 29, 3, 37, 3, 43, 83, 3, 3, 89, 5, 97, 191, 293, 7, 491, 7

Offset: 1

N. J. A. Sloane, Dec 16 2010

nonn

Has period 69, starting with the fourth term: 3, 5, 3, 11, 19, 3, 3, 5, 11, ...

Cf. A178094, A020639, A175723, A177904.

nxt[{a_,b_,c_}]:={b,c,FactorInteger[a+b+c][[1,1]]}; Transpose[ NestList[ nxt,{1,1,1},100]][[1]] (* Harvey P. Dale, Aug 19 2014 *)

cp's OEIS Frontend

A175723 a(1)=a(2)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)), where gpf = "greatest prime factor".

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