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

1,1

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

Mathematica

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

Prog

(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")

Crossrefs

Sequence in context: A091157 A199336 A214876 * A036952 A065720 A148554

Adjacent sequences: A280270 A280271 A280272 * A280274 A280275 A280276

Keyword

nonn

Author

Ely Golden, Dec 30 2016

Status

approved