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 A072926 #20 Apr 18 2025 21:30:12
%S A072926 1,1,1,2,2,3,3,4,6,7,7,8,8,9,11,12,12,13,13,14,16,17,17,18,20,23,25,
%T A072926 26,26,27,27,28,30,33,35,36,36,37,39,40,40,41,41,42,44,45,45,46,48,51,
%U A072926 53,54,54,55,57,60,62,63,63,64,64,65,67,70,72,73,73,74,76,77,77,78,78,79
%N A072926 a(n) = Sum_{k=1..n} A051699(k).
%H A072926 Amiram Eldar, <a href="/A072926/b072926.txt">Table of n, a(n) for n = 1..10000</a>
%F A072926 Conjecture: a(n) is asymptotic to C*n*log(n) with C = 0.29... .
%F A072926 From _Ya-Ping Lu_, Apr 06 2025: (Start)
%F A072926 C = lim_{n->oo} a(n)/(n*log(n)) = 0.44 approximately.
%F A072926 a(prime(m)) = 1 + Sum_(i=3..m) (1/4)*(prime(i)-prime(i-1))^2. (End)
%t A072926 f[n_] := If[PrimeQ[n], 0, Min[NextPrime[n] - n, n - NextPrime[n, -1]]]; Accumulate[Table[f[n], {n, 1, 100}]] (* _Amiram Eldar_, May 05 2022 *)
%o A072926 (PARI) a(n)=sum(k=1,n,vecmin(vector(k,i,abs(k-prime(i)))))
%o A072926 (Python)
%o A072926 from sympy import nextprime; p = a = 1
%o A072926 while p < 71:
%o A072926 q = nextprime(p); h = (q - p)//2
%o A072926 for i in range(q-p): a += h - abs(h-i); print(a, end = ', ')
%o A072926 p = q # _Ya-Ping Lu_, Apr 06 2025
%Y A072926 Cf. A051699.
%K A072926 nonn
%O A072926 1,4
%A A072926 _Benoit Cloitre_, Aug 11 2002