A375864 Prime numbers that cannot be written as the sum of a prime number and a superior highly composite number.

2, 3, 307, 911, 1201, 1259, 1693, 2179, 2381, 2927, 3191, 3499, 3557, 4201, 4441, 4721, 5573, 6121, 7207, 8219, 8273, 8537, 8627, 8999, 9137, 9203, 9811, 10133, 10357, 11597, 12211, 12343, 13217, 13421, 13921, 15053, 15401, 15551, 15959, 15991, 16411, 16561, 17117, 17207

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Example

The prime number 37 can be written as the sum of prime number 31 and superior highly composite number 6 and thus is not in this sequence.

Prog

(Python)
from sympy import *
SHCN = [2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720]
for x in range(3, 16000, 2):
    waysFound = 0
    if isprime(x):
        iterC = 0
        while iterC < len(SHCN) and SHCN[iterC] < x:
            if isprime(x - SHCN[iterC]):
                waysFound += 1
            iterC += 1
        if waysFound == 0:
            print(x)

Crossrefs

Cf. A000040, A002201, A375866.

Sequence in context: A307212 A377031 A177505 * A068104 A065586 A375236

Adjacent sequences: A375861 A375862 A375863 * A375865 A375866 A375867

Keyword

nonn

Author

Walter Robinson, Aug 31 2024

Status

approved