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

0,4

Comments

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

Links

Table of n, a(n) for n=0..69.

Index entries for periodic sequences.

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).

Formula

G.f.: x*(1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 8*x^5 + 13*x^6 + 3*x^7 + 16*x^8 + 19*x^9 + 5*x^10 + 24*x^11 + 29*x^12 + 53*x^13 + 2*x^14 + 5*x^15 + 7*x^16 + 12*x^17 + 19*x^18 + 31*x^19 + 50*x^20 + 81*x^21 + 131*x^22 + 212*x^23 + 343*x^24 + 555*x^25 + 2*x^26 + 557*x^27 + 13*x^28 + 570*x^29 + 11*x^30 + 7*x^31 + 18*x^32 + 5*x^33 + 23*x^34 + 28*x^35 + 2*x^36 + 30*x^37)/(1 - x^36). - Charles R Greathouse IV, May 21 2026

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 *)

Crossrefs

Cf. A214094.

Sequence in context: A287533 A072123 A135102 * A078414 A254056 A238948

Adjacent sequences: A214153 A214154 A214155 * A214157 A214158 A214159

Keyword

nonn,easy

Author

Vladimir Shevelev, Feb 16 2013

Status

approved