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 A005236 M0501 #42 Sep 07 2023 04:45:11 %S A005236 2,3,4,5,6,8,9,10,12,14,17,18,20,24,26,28,30,33,38,42,48,50,54,60,65, %T A005236 74,82,84,90,98,102,108,110,114,126,129,138,150,164,168,174,180,194, %U A005236 198,228,234,244,252,258,264,270,290,294,318,348,354,360,384,390,402 %N A005236 Barriers for omega(n): numbers n such that, for all m < n, m + omega(m) <= n. %C A005236 omega(m) is the number of distinct prime factors of m. %D A005236 R. K. Guy, Unsolved Problems in Number Theory, B8. %D A005236 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A005236 Charles R Greathouse IV, <a href="/A005236/b005236.txt">Table of n, a(n) for n = 1..10000</a> %H A005236 Paul Erdős, <a href="https://www.jstor.org/stable/2689842">Some Unconventional Problems in Number Theory</a>, Mathematics Magazine, Vol. 52, No. 2, Mar., 1979, pp. 67-70. See Problem 4, p. 68. %H A005236 Paul Erdős, <a href="https://users.renyi.hu/~p_erdos/1979-23.pdf">Some unconventional problems in number theory</a>, Acta Mathematica Hungarica, 33(1):71-80, 1979. %e A005236 1 + omega(1) = 1, 2 + omega(2) = 3, 3 + omega(3) = 4, 4 + omega(4) = 5, 5 + omega(5) = 6. %e A005236 Thus we have verified that m + omega(m) < 6 for m < 6, so 6 is in the sequence. %e A005236 But since 6 + omega(6) = 8 > 7, 7 is not in the sequence. %t A005236 omegaBarrierQ[n_] := (For[m = 1, m < n, m++, If[m + PrimeNu[m] > n, Return[False]]]; True); Select[Range[2, 500], omegaBarrierQ] (* _Jean-François Alcover_, Feb 03 2015 *) %o A005236 (PARI) is(n)=for(k=1,log(n)\log(5),if(omega(n-k)>k,return(0)));n>1 \\ _Charles R Greathouse IV_, Sep 19 2012 %o A005236 (Haskell) %o A005236 a005236 n = a005236_list !! (n-1) %o A005236 a005236_list = filter (\x -> all (<= x) $ map a229109 [1..x-1]) [2..] %o A005236 -- _Reinhard Zumkeller_, Sep 13 2013 %Y A005236 Cf. A001221, A229109. %K A005236 nonn,nice %O A005236 1,1 %A A005236 _N. J. A. Sloane_ %E A005236 More terms from _John W. Layman_