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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 Table of n, a(n) for n=0..69. 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 Adjacent sequences: A214153 A214154 A214155 * A214157 A214158 A214159 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.)