A063643 -id:A063643 - cp's OEIS frontend

A277993 Sophie Germain primes p such that p + 2 and p - 2 are semiprimes.

23, 53, 89, 113, 131, 251, 293, 491, 683, 719, 953, 1439, 1499, 1511, 1733, 2393, 3491, 3779, 5171, 7043, 7151, 7433, 7649, 7901, 8069, 8663, 9689, 10781, 12011, 12653, 13049, 13229, 13451, 13553, 14669, 15569, 16001, 16253, 18899, 19709, 20411, 22469, 22751, 23099

Offset: 1

K. D. Bajpai, Nov 07 2016

nonn

Intersection of A005384 and A063643.

			a(1) = 23 is Sophie Germain prime because 2*23 + 1 = 47 is prime. Also, 23 + 2 = 25 =  5*5; 23 - 2 = 21 = 7*3; are both semiprime.
a(2) = 53 is Sophie Germain prime because 2*53 + 1 = 107 is prime. Also, 53 + 2 = 55 =  11*5; 23 - 2 = 51 = 17*3; are both semiprime.

K. D. Bajpai, Table of n, a(n) for n = 1..4000

Cf. A005384, A063637, A063638, A063643.

Select[Select[Prime[Range[10000]], PrimeQ[2 # + 1] &], PrimeOmega[# - 2] == 2 && PrimeOmega[# + 2] == 2 &]
Select[Prime[Range[3000]],PrimeQ[2#+1]&&PrimeOmega[#+{2,-2}]=={2,2}&] (* Harvey P. Dale, Dec 16 2017 *)

is(n) = ispseudoprime(n) && ispseudoprime(2*n+1) && bigomega(n+2)==2 && bigomega(n-2)==2 \\ Felix Fröhlich, Nov 07 2016

A369957 Primes p such that p - 3 and p + 3 are triprimes.

Original entry on oeis.org

47, 73, 113, 127, 151, 167, 233, 239, 241, 313, 409, 431, 433, 439, 521, 593, 599, 601, 607, 719, 727, 967, 1031, 1087, 1249, 1409, 1439, 1471, 1559, 1601, 1831, 1913, 1993, 2089, 2161, 2273, 2281, 2287, 2311, 2351, 2393, 2633, 2689, 2711, 2729, 2767, 2833, 2879, 3079, 3313, 3319, 3359, 3511

Offset: 1

Zak Seidov and Robert Israel, Feb 07 2024

nonn

Primes p such that p - 3 and p + 3 each have 3 prime factors, counted with multiplicity.

Primes p such that one of p - 3 and p + 3 is 4 times a prime and the other is 2 times a semiprime.

			a(3) = 113 is a term because 113 is prime, and 110 = 2 * 5 * 11 and 116 = 2^2 * 29 are triprimes.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001222, A014612, A063643.

filter:= proc(n)
  isprime(n) and numtheory:-bigomega(n-3) = 3 and numtheory:-bigomega(n+3) = 3
end proc:
select(filter, [seq(i,i=3..20000,2)]);

s = {}; p = 5; Do[If[{3, 3} == PrimeOmega[{p - 3, p + 3}],
AppendTo[s, p]]; p = NextPrime[p], {500}]; s
Select[Prime[Range[500]],PrimeOmega[#-3]==PrimeOmega[#+3]==3&]

A115396 Smallest prime p such that p+-2n are semiprimes.

Original entry on oeis.org

23, 29, 71, 17, 59, 37, 71, 41, 67, 71, 43, 109, 59, 67, 173, 83, 89, 151, 103, 89, 127, 101, 131, 113, 127, 109, 131, 113, 127, 193, 157, 157, 181, 179, 229, 163, 193, 191, 211, 223, 223, 239, 241, 211, 211, 211, 271, 281, 241, 241, 263, 307, 307, 373, 293

Offset: 1

Zak Seidov, Mar 08 2006

nonn

Cf. A063643 Primes p such that p+-2 are semiprimes, A117328 Primes p such that p+-4 are semiprimes.

			a(100)=571 because 571-2*100=371=7*53 (semiprime), 571+2*100=771=3*257 (semiprime).

Cf. A063643.

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A277993 Sophie Germain primes p such that p + 2 and p - 2 are semiprimes.

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A369957 Primes p such that p - 3 and p + 3 are triprimes.

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A115396 Smallest prime p such that p+-2n are semiprimes.

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