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A180931
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Primes p such that their product for the successive prime plus one added to one is a prime: p(i)*[p(i+1)+1]+1 gives a prime.
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2
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3, 5, 19, 23, 29, 47, 53, 59, 79, 137, 167, 179, 233, 239, 241, 263, 283, 349, 353, 359, 383, 389, 419, 421, 439, 491, 563, 617, 653, 701, 709, 719, 739, 769, 797, 811, 829, 887, 1049, 1051, 1129, 1153, 1187, 1399, 1433, 1489, 1523, 1549, 1559, 1579, 1601
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OFFSET
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1,1
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COMMENTS
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There are some twin primes in the sequence: (3,5); (239,241); (419, 421); (1607, 1609).
Apparently the sequence is infinite.
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LINKS
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EXAMPLE
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a(5)=29 since 29*(31+1)+1=29*32+1=929 is a prime.
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MAPLE
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R:= NULL; count:= 0:
q:= 2:
while count < 100 do
p:= q; q:= nextprime(q);
if isprime(p*(q+1)+1) then count:= count+1; R:= R, p fi
od:
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MATHEMATICA
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Select[Prime[Range[350]], PrimeQ[ # (NextPrime[ # ]+1)+1]&] (* Harvey P. Dale, Oct 08 2010 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Added missing terms (5 terms were omitted after 887). Harvey P. Dale, Oct 08 2010
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STATUS
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approved
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