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A370090
Numbers that can be expressed in exactly one way as the unordered sum of two distinct primes.
1
5, 7, 8, 9, 10, 12, 13, 14, 15, 19, 21, 25, 31, 33, 38, 39, 43, 45, 49, 55, 61, 63, 69, 73, 75, 81, 85, 91, 99, 103, 105, 109, 111, 115, 129, 133, 139, 141, 151, 153, 159, 165, 169, 175, 181, 183, 193, 195, 199, 201, 213, 225, 229, 231, 235, 241, 243, 253, 259, 265
OFFSET
1,1
COMMENTS
Apparently, a number that is the predecessor or successor of a prime number does not have a sum as defined here, except for a finite number of primes, which may be {7, 11, 13, 37}. - Peter Luschny, Feb 16 2024
EXAMPLE
5 = 2+3; 7 = 2+5; 8 = 3+5; 9 = 2+7; 10 = 3+7 (10 = 5+5 is not considered).
MAPLE
select(n -> A117929(n) = 1, [seq(1..265)]); # Peter Luschny, Feb 16 2024
PROG
(Python)
from sympy import sieve
from collections import Counter
from itertools import combinations
def aupton(max):
sieve.extend(max)
a = Counter(c[0]+c[1] for c in combinations(sieve._list, 2))
return [n for n in range(1, max+1) if a[n] == 1]
print(aupton(265)) # Michael S. Branicky, Feb 16 2024
CROSSREFS
Cf. A117929, A048974, A065091, A067187 (not necessarily distinct).
If we change 1 way (this sequence) we get A077914 (2 ways), A077969 (3 ways), A078299 (4 ways), A080854 (5 ways), and A080862 (6 ways).
Sequence in context: A243624 A038609 A078892 * A164374 A072281 A242273
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Feb 11 2024
STATUS
approved