A280273 Primes p such that 8p^2 - 7p + 2 is also prime.

3, 5, 23, 41, 59, 113, 131, 173, 179, 269, 281, 383, 401, 431, 443, 449, 461, 479, 521, 641, 653, 863, 929, 941, 953, 1013, 1103, 1163, 1301, 1319, 1361, 1439, 1481, 1559, 1583, 1871, 2003, 2213, 2309, 2411, 2609, 2693, 2711, 2729, 2801, 2903, 2909, 2969, 3041

Offset: 1

Author

Ely Golden, Dec 30 2016

Keywords

• nonn

Comments

For any p in this sequence, 2*p*(8p^2 - 7p + 2) has the same nonzero digits as its prime factors in base 2*p-1.

Apart from 3 itself, all members of this sequence are congruent to 2 (mod 3). This is because for any number congruent to 1 (mod 3), the expression (8n^2 - 7n + 2) would be a multiple of 3 and hence not prime.

Links

• Ely Golden, Table of n, a(n) for n = 1..1000

Programs

Mathematica

Select[Prime@ Range@ 450, PrimeQ[8 #^2 - 7 # + 2] &] (* Michael De Vlieger, Dec 30 2016 *)

SageMath

c=1
index=1
while(index<=1000):
    if((is_prime(c))&(is_prime(8*(c**2)-7*c+2))):
        print(str(index)+" "+str(c))
        index+=1
    c+=1
print("complete")