A381330 Numbers that are the sum of a prime and the square of a prime in more than one way.

11, 27, 28, 32, 38, 51, 52, 54, 56, 62, 66, 68, 72, 78, 80, 86, 92, 96, 98, 108, 110, 116, 122, 126, 128, 132, 134, 138, 140, 146, 150, 152, 156, 158, 162, 164, 171, 172, 174, 176, 180, 182, 186, 188, 192, 198, 200, 204, 206, 210, 212, 216, 218, 222, 224, 228

Offset

1,1

Comments

Subsequence of A081053. Most terms are even. The odd terms are 11, 27, 51, 171, 363, 843, 1371, 1851 and must be of the form 2+p^2=4+q for primes p, q. In particular, the odd terms are exactly A049002(n)+4 for n>1.

Links

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

Example

11 is a term since 11 = 2^2+7  = 3^2+2.
27 is a term since 27 = 2^2+23 = 5^2+2.
28 is a term since 28 = 3^2+19 = 5^2+3.
32 is a term since 32 = 3^2+23 = 5^2+7.

Prog

(Python)
from math import isqrt
from itertools import count, islice
from sympy import isprime, primerange
def A381330_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue, 1)):
        c = 0
        for p in primerange(isqrt(n)+1):
            if isprime(n-p**2):
                c += 1
            if c>1:
                yield n
                break
A381330_list = list(islice(A381330_gen(), 30))
(PARI) isok(k) = my(nb=0); forprime(p=2, sqrtint(k), if (isprime(k-p^2), nb++); ); nb > 1; \\ Michel Marcus, Feb 21 2025

Crossrefs

Cf. A081053, A049002.

Sequence in context: A014468 A156373 A368930 * A029492 A185451 A165608

Adjacent sequences: A381327 A381328 A381329 * A381331 A381332 A381333

Keyword

nonn

Author

Chai Wah Wu, Feb 20 2025

Status

approved