A246824 - OEIS

%I #22 Sep 08 2019 15:20:33

%S 3,35,41,52,57,81,104,209,215,343,373,398,473,477,584,628,768,774,828,

%T 872,1117,1145,1189,1287,1324,1435,1615,1634,1653,1704,1886,1925,2070,

%U 2075,2123,2171,2193,2425,2449,2605,2633,2934,2948,3019,3194,3273,3533,3552,3685,3758

%N Numbers k for which A242720(k) = (prime(k)+1)^2 + 2.

%C By a comment in A246748, A242720(k) >= (prime(k)+1)^2 + 2, and equality is attained in this sequence.

%C Prime(a(n)) >= 5 and is in the intersection of A001359 and A157468.

%H Chai Wah Wu, <a href="/A246824/b246824.txt">Table of n, a(n) for n = 1..10000</a>

%t lpf[n_] := FactorInteger[n][[1, 1]]; aQ[n_] := Module[{k=6}, While[PrimeQ[k-3] && PrimeQ[k-1] || lpf[k-1]<=lpf[k-3] || lpf[k-3]<Prime[n], k+=2]; k == (Prime[n]+1)^2 + 2]; Select[Range[50], aQ] (* _Amiram Eldar_, Dec 10 2018 *)

%o (PARI) lpf(k) = factorint(k)[1, 1];

%o f(n) = my(k=6); while((isprime(k-3) && isprime(k-1)) || lpf(k-1)<=lpf(k-3) || lpf(k-3)<prime(n), k+=2); k; \\ A242720

%o isok(n) = f(n) == (prime(n)+1)^2 + 2; \\ _Michel Marcus_, Dec 10 2018

%o (Python)

%o from sympy import prime, isprime, factorint

%o A246824_list = [a for a, b in ((n, prime(n)+1) for n in range(3,10**3)) if (not (isprime(b**2-1) and isprime(b**2+1)) and (min(factorint(b**2+1)) > min(factorint(b**2-1)) >= b-1))] # _Chai Wah Wu_, Jun 03 2019

%Y Cf. A001359, A157468, A242719, A242720, A246748, A246819, A246821.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Sep 04 2014

%E a(40)-a(50) from b-file by _Robert Price_, Sep 08 2019