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A221218 Let sequence B_n={b_m} be defined by: b_1=prime(n), b_2=prime(n+1); for m>=3, b_m=b_(m-2)+b_(m-1) if b_(m-2)+b_(m-1) is not semiprime, otherwise b_m is the least prime divisor of b_(m-2)+b_(m-1). Then a(n) is the maximal term of sequence B_n, or a(n)=0 if B_n is unbounded. 0

%I

%S 570,570,570,570,19726,113750,570,22534,570,570,570,570,399610,570,

%T 570,570,3138,670,570,570,772,570,570,2448,109472,570,570,570,1150,

%U 609,18644,71049,2276,570,1634,1552,13844,798,68830,6940,575,1498,668,2551,1586,29729,1748,113750,19726,1435,194650,64360,3213,953988,9146,16539,811,8370238,516878,881,99942,7399,4160,215843,8397,676,13397,1715,915722,702,3572,141759,1192,1131,762,24895,1194,22534,1750,7069,68830

%N Let sequence B_n={b_m} be defined by: b_1=prime(n), b_2=prime(n+1); for m>=3, b_m=b_(m-2)+b_(m-1) if b_(m-2)+b_(m-1) is not semiprime, otherwise b_m is the least prime divisor of b_(m-2)+b_(m-1). Then a(n) is the maximal term of sequence B_n, or a(n)=0 if B_n is unbounded.

%C Conjecture: All a(n)>=570. Conjecture: All sequences B_n are eventually periodic.

%C Moreover, our first observations show that up to n=8, the lengths of the periods is 36.

%C _Peter J. C. Moses_ extended these observations and confirmed the same length 36 of all periods up to n=209.

%e In case n=1, B_1 essentially coincides with A214156 and thus a(1)=570 which is the maximal term of A214156.

%Y Cf. A214156.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Feb 22 2013

%E Terms beginning with a(5) from _Peter J. C. Moses_

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Last modified September 26 15:51 EDT 2022. Contains 357000 sequences. (Running on oeis4.)