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A079149
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Primes p such that either p-1 or p+1 has at most 2 prime factors, counted with multiplicity; i.e. primes p such that either bigomega(p-1) <= 2 or bigomega(p+1) <= 2, where bigomega(n) = A001222(n).
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4
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2, 3, 5, 7, 11, 13, 23, 37, 47, 59, 61, 73, 83, 107, 157, 167, 179, 193, 227, 263, 277, 313, 347, 359, 383, 397, 421, 457, 467, 479, 503, 541, 563, 587, 613, 661, 673, 719, 733, 757, 839, 863, 877, 887, 983, 997, 1019, 1093, 1153, 1187, 1201, 1213, 1237
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| There are only 2 primes such that both p-1 and p+1 have at most 2 prime factors - 3 and 5. Proof: If p>5 then whichever of p-1 and p+1 is divisible by 4 has at least 3 prime factors.
Primes which not are the sum of two consecutive composite numbers. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 15 2009]
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MATHEMATICA
| Select[Prime[Range[500]], MemberQ[PrimeOmega[{#-1, #+1}], 2]&] (* From Harvey P. Dale, Sep 04 2011 *)
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PROG
| (PARI) s(n) = {sr=0; ct=0; forprime(x=2, n, if(bigomega(x-1) < 3 || bigomega(x+1) < 3, print1(x" "); sr+=1.0/x; ct+=1; ); ); print(); print(ct" "sr); } \\ Lists primes p<=n such that p+-1 has at most 2 prime factors.
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CROSSREFS
| Union of A079147 and A079148. Cf. A079152.
Cf. A060254. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 15 2009]
Sequence in context: A087634 A178576 A038970 * A024694 A024320 A111252
Adjacent sequences: A079146 A079147 A079148 * A079150 A079151 A079152
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KEYWORD
| easy,nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Dec 27 2002
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