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 A385724 #10 Jul 13 2025 15:36:15
%S A385724 17,2,5,10,1547,8837,1293224,52445796,3267037,896531141,183208285259
%N A385724 The least integer of n consecutive numbers where each has its sum of prime factors, with multiplicity, being a prime.
%C A385724 According to Primepuzzles, puzzle 445:
%C A385724 a(10) = 896531141 given by _Carlos Rivera_.
%C A385724 a(11) = 183208285259 given by _Jens Kruse Andersen_.
%H A385724 Fang, <a href="https://www.zhihu.com/question/1925579031916552491">Can we find that the sum of prime factors of each of twelve consecutive positive integers is a prime number?</a>
%H A385724 G. L. Honaker, Jr., <a href="https://t5k.org/curios/page.php?number_id=9476">Prime Curio 183208285259</a>.
%H A385724 Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_445.htm">Puzzle 445. Consecutive integers with prime SPF</a>, The Prime Puzzles & Problems Connection.
%e A385724 a(4) = 10 because 10=2*5, 11=11, 12 = 2^2*3, 13 = 13 and sum of prime factors of the four consecutive numbers are all primes : 2 + 5 = 7, 11, 2 + 2 + 3 = 7, 13.
%t A385724 f[n_] := PrimeQ@Total[Times @@@ FactorInteger[n]]; a = Table[0, 6];
%t A385724 c = 0; Do[If[c == 0, s = n]; If[f[n] == False, If[a[[c]] == 0, a[[c]] = s]; c = 0, c++], {n, 2, 10000}]; a
%Y A385724 Cf. A100118, A337310.
%K A385724 nonn,more
%O A385724 1,1
%A A385724 _Zhining Yang_, Jul 08 2025