cp's OEIS Frontend

A370090 Numbers that can be expressed in exactly one way as the unordered sum of two distinct primes.

%I A370090 #47 Dec 30 2024 19:18:35
%S A370090 5,7,8,9,10,12,13,14,15,19,21,25,31,33,38,39,43,45,49,55,61,63,69,73,
%T A370090 75,81,85,91,99,103,105,109,111,115,129,133,139,141,151,153,159,165,
%U A370090 169,175,181,183,193,195,199,201,213,225,229,231,235,241,243,253,259,265
%N A370090 Numbers that can be expressed in exactly one way as the unordered sum of two distinct primes.
%C A370090 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
%H A370090 Michael S. Branicky, <a href="/A370090/b370090.txt">Table of n, a(n) for n = 1..10000</a>
%H A370090 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A370090 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%e A370090 5 = 2+3; 7 = 2+5; 8 = 3+5; 9 = 2+7; 10 = 3+7 (10 = 5+5 is not considered).
%p A370090 select(n -> A117929(n) = 1, [seq(1..265)]);  # _Peter Luschny_, Feb 16 2024
%t A370090 tdpQ[{a_,b_}]:=AllTrue[{a,b},PrimeQ]&&a!=b; Select[Range[300],Count[IntegerPartitions[#,{2}],_?tdpQ]==1&] (* _Harvey P. Dale_, Dec 30 2024 *)
%o A370090 (Python)
%o A370090 from sympy import sieve
%o A370090 from collections import Counter
%o A370090 from itertools import combinations
%o A370090 def aupton(max):
%o A370090     sieve.extend(max)
%o A370090     a = Counter(c[0]+c[1] for c in combinations(sieve._list, 2))
%o A370090     return [n for n in range(1, max+1) if a[n] == 1]
%o A370090 print(aupton(265)) # _Michael S. Branicky_, Feb 16 2024
%Y A370090 Cf. A117929, A048974, A065091, A067187 (not necessarily distinct).
%Y A370090 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).
%K A370090 nonn
%O A370090 1,1
%A A370090 _Wesley Ivan Hurt_, Feb 11 2024