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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. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
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).
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Feb 16 2013
STATUS
approved

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Last modified July 24 03:05 EDT 2024. Contains 374575 sequences. (Running on oeis4.)