A063643 - OEIS

A063643

Primes with 2 representations: p*q - 2 = u*v + 2 where p, q, u and v are primes.

23, 37, 53, 67, 89, 113, 131, 157, 211, 251, 293, 307, 337, 379, 409, 449, 487, 491, 499, 503, 631, 683, 701, 719, 751, 769, 787, 919, 941, 953, 991, 1009, 1039, 1117, 1193, 1201, 1259, 1381, 1399, 1439, 1459, 1471, 1499, 1511, 1567, 1709, 1733, 1759, 1801

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Or, primes p such that p+/-2 are semiprimes. - Zak Seidov, Mar 08 2006

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 term from T. D. Noe)

FORMULA

Intersection of A063637 and A063638. - Zak Seidov, Mar 14 2011

EXAMPLE

A063643(25) = 751: 751 = A063637(60)= 753 - 2 = 3*251 - 2, 751 = A063638(55)= 749 + 2 = 7*107 + 2.

MAPLE

q:= p-> isprime(p) and map(numtheory[bigomega], {p-2, p+2})={2}:

select(q, [$2..2000])[]; # Alois P. Heinz, Apr 01 2024

MATHEMATICA

Select[Prime[Range[300]], PrimeOmega[#+2] == PrimeOmega[#-2] == 2&] (* Jean-François Alcover, Mar 02 2019 *)

PROG

(PARI) { n=0; for (m=2, 10^9, p=prime(m); if (bigomega(p + 2) == 2 && bigomega(p - 2) == 2, write("b063643.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 26 2009

CROSSREFS

Cf. A063637, A063638, A001358.

Cf. A109611 (Chen primes).

Sequence in context: A055114 A329262 A268343 * A361530 A057876 A244282

Adjacent sequences: A063640 A063641 A063642 * A063644 A063645 A063646

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 21 2001

STATUS

approved