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.
%I A054265 #38 Jun 01 2024 20:02:25 %S A054265 0,4,6,27,12,45,18,63,130,30,170,117,42,135,250,280,60,320,207,72,380, %T A054265 243,430,651,297,102,315,108,333,1560,387,670,138,1296,150,770,800, %U A054265 495,850,880,180,1674,192,585,198,2255,2387,675,228,693,1180,240,2214,1270 %N A054265 Sum of composite numbers between successive primes. %H A054265 James Spahlinger, <a href="/A054265/b054265.txt">Table of n, a(n) for n = 1..1000</a> %H A054265 Paul Barry, <a href="https://arxiv.org/abs/2104.05593">On the Gap-sum and Gap-product Sequences of Integer Sequences</a>, arXiv:2104.05593 [math.CO], 2021. %F A054265 a(n) = (prime(n+1) + prime(n))*(prime(n+1) - prime(n) - 1)/2. - _Zak Seidov_, Sep 12 2002 %e A054265 Between 7 and 11 we have 8 + 9 + 10 which is a(4)=27. %o A054265 (PARI) a(n) = (prime(n+1) + prime(n))*(prime(n+1) - prime(n) - 1)/2; \\ _Michel Marcus_, Mar 24 2016 %o A054265 (Python) %o A054265 from sympy import nextprime, prime %o A054265 def A054265(n): return ((p:=prime(n))+(q:=nextprime(p)))*(q-p-1)>>1 # _Chai Wah Wu_, Jun 01 2024 %Y A054265 Cf. A000040, A046933, A054264, A054266, A054267, A054268. %K A054265 nonn %O A054265 1,2 %A A054265 _Patrick De Geest_, Apr 15 2000