This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
22 is a term as 22 = 19+3 = 17+5 are the only two ways to express 22 as a sum of two distinct primes.
66 is a term as 66 = 37 + 29 = 43 + 23 = 47 + 17 = 53 + 13 = 59 + 7 = 61 + 5 are only the six ways to express 66 as a sum of two distinct primes.
tdpQ[n_]:=Count[IntegerPartitions[n,{2}],?(AllTrue[#,PrimeQ]&&Length[Union[#]]==2&)]==6; Select[Range[400],tdpQ] (* _Harvey P. Dale, Aug 17 2025 *)
30 is a term as 30 = 23+7 = 19+11 = 17+13 are the only three ways to express 30 as a sum of three distinct primes.
36 is a term as 36 = 31 + 5 = 29 + 7 = 23 + 13 = 19 + 17 are only the four ways to express 36 as a sum of two distinct primes.
a(5) = 188 because 188 = 7 + 181 = 31 + 157 = 37 + 151 = 61 + 127 = 79 + 109 and it is conjectured that 188 is the last term of A080854.
5 = 2+3; 7 = 2+5; 8 = 3+5; 9 = 2+7; 10 = 3+7 (10 = 5+5 is not considered).
select(n -> A117929(n) = 1, [seq(1..265)]); # Peter Luschny, Feb 16 2024
tdpQ[{a_,b_}]:=AllTrue[{a,b},PrimeQ]&&a!=b; Select[Range[300],Count[IntegerPartitions[#,{2}],?tdpQ]==1&] (* _Harvey P. Dale, Dec 30 2024 *)
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
Comments