A214156 Dual to A214094: a(0)=0, a(1)=1; a(n) = a(n-1) + a(n-2) if a(n-1) + a(n-2) is not semiprime; a(n) is minimal prime divisor of a(n-1) + a(n-2) if a(n-1) + a(n-2) is semiprime.

0, 1, 1, 2, 3, 5, 8, 13, 3, 16, 19, 5, 24, 29, 53, 2, 5, 7, 12, 19, 31, 50, 81, 131, 212, 343, 555, 2, 557, 13, 570, 11, 7, 18, 5, 23, 28, 3, 31, 2, 3, 5, 8, 13, 3, 16, 19, 5, 24, 29, 53, 2, 5, 7, 12, 19, 31, 50, 81, 131, 212, 343, 555, 2, 557, 13, 570, 11, 7, 18

Offset: 0

Author

Vladimir Shevelev, Feb 16 2013

Keywords

• nonn

Comments

The sequence has period of length 36: {2,3,5,...,28,3,31} and thus is bounded.

Links

• Index entries for linear recurrences with constant coefficients, signature (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, 0, 1).

Crossrefs

Cf. A214094.

Programs

Mathematica

A214156[0]:=0; A214156[1]:=1; A214156[n_] := A214156[n] = If[PrimeOmega[#] == 2, First[Rest[Divisors[#]]], #]& [A214156[n-1] + A214156[n-2]]; Table[A214156[n], {n,0,99}] (* Peter J. C. Moses, Feb 18 2013 *)
nxt[{a_,b_}]:={b,If[PrimeOmega[a+b]==2,FactorInteger[a+b][[1,1]],a+b]}; NestList[nxt,{0,1},70][[All,1]] (* or *) PadRight[{0,1,1},70,{28,3,31,2,3,5,8,13,3,16,19,5,24,29,53,2,5,7,12,19,31,50,81,131,212,343,555,2,557,13,570,11,7,18,5,23}] (* Harvey P. Dale, Feb 02 2017 *)