A246824 Numbers k for which A242720(k) = (prime(k)+1)^2 + 2.

3, 35, 41, 52, 57, 81, 104, 209, 215, 343, 373, 398, 473, 477, 584, 628, 768, 774, 828, 872, 1117, 1145, 1189, 1287, 1324, 1435, 1615, 1634, 1653, 1704, 1886, 1925, 2070, 2075, 2123, 2171, 2193, 2425, 2449, 2605, 2633, 2934, 2948, 3019, 3194, 3273, 3533, 3552, 3685, 3758

Offset: 1

Author

Vladimir Shevelev, Sep 04 2014

Keywords

• nonn

Comments

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

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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]Amiram Eldar, Dec 10 2018 *)

PARI

lpf(k) = factorint(k)[1, 1];
f(n) = my(k=6); while((isprime(k-3) && isprime(k-1)) || lpf(k-1)<=lpf(k-3) || lpf(k-3)A242720
isok(n) = f(n) == (prime(n)+1)^2 + 2; \\ Michel Marcus, Dec 10 2018

Python

from sympy import prime, isprime, factorint
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

Extensions

a(40)-a(50) from b-file by Robert Price, Sep 08 2019