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A365537
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a(n) is the first semiprime k such that k-1 and k+1 each have exactly n prime factors (counted with multiplicity).
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0
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4, 34, 51, 55, 1169, 6641, 18751, 204929, 101249, 2490751, 6581249, 68068351, 262986751, 1842131969, 9601957889, 13858918399, 145046192129, 75389157377, 18444674957311, 39806020354049, 124758724247551, 878616032837633, 551785225781249
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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a(3) = 51 because 51 = 3 * 17 is a semiprime and 50 - 1 = 50 = 2 * 5^2 and 51 + 1 = 52 = 2^2 * 13 are triprimes.
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MAPLE
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V:= Vector(10): count:= 0:
b:= 1: c:= 2:
for x from 5 while count < 10 do
a:= b; b:= c; c:= numtheory:-bigomega(x);
if b = 2 and a = c and V[a] = 0 then
count:= count+1; V[a]:= x-1; printf("%d %d\n", a, x-1);
fi
od:
convert(V, list);
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MATHEMATICA
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seq[len_, kmax_] := Module[{s = Table[0, {len}], k = 2, c = 0, m}, While[c < len && k < kmax, If[PrimeOmega[k] == 2, m = PrimeOmega[k - 1]; If[m <= len && s[[m]] == 0 && PrimeOmega[k + 1] == m, c++; s[[m]] = k]]; k++]; s]; seq[10, 10^7] (* Amiram Eldar, Sep 08 2023 *)
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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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STATUS
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approved
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