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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
570, 570, 570, 570, 19726, 113750, 570, 22534, 570, 570, 570, 570, 399610, 570, 570, 570, 3138, 670, 570, 570, 772, 570, 570, 2448, 109472, 570, 570, 570, 1150, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

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

LINKS

Table of n, a(n) for n=1..81.

EXAMPLE

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

CROSSREFS

Cf. A214156.

Sequence in context: A240715 A263708 A219992 * A252465 A252473 A252466

Adjacent sequences:  A221215 A221216 A221217 * A221219 A221220 A221221

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Feb 22 2013

EXTENSIONS

Terms beginning with a(5) from Peter J. C. Moses

STATUS

approved

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Last modified August 16 07:50 EDT 2022. Contains 356160 sequences. (Running on oeis4.)