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A247461 Subsequence obtained from A026242 by applying an Eratosthenes-type sieve: strike out every second number after the first "2", then if m is the next number not yet struck out, strike out every m-th number following this one, etc.

%I A247461 #20 Dec 23 2024 14:53:44
%S A247461 1,1,2,3,4,5,8,15,20,35,50,37,40,46,109,124,134,92,183,198,223,159,
%T A247461 272,282,205,214,356,371,406,445,480,495,312,321,569,579,367,628,653,
%U A247461 434,742,801,816,851,535,925,940,587,596,999,1014,1024,709,755,1261
%N A247461 Subsequence obtained from A026242 by applying an Eratosthenes-type sieve: strike out every second number after the first "2", then if m is the next number not yet struck out, strike out every m-th number following this one, etc.
%C A247461 The first two terms a(1)=a(2)=1 are included here but are not considered to be part of what one might call  A026242-primes, in analogy of the usual primes A000040 obtained by applying the very same procedure to the set of all positive integers.
%C A247461 Since A026242 is not increasing, this sequence isn't, either. However, since the remaining "primes" > 1 are exactly the numbers used during the sieve, and for all m, the second m occurs m places after the first m in A026242, no number can occur twice here.
%C A247461 There is a stronger version of the sieve, which consists of considering all numbers "m", whether or not they have been crossed out earlier. When this is applied, then the result is the finite subsequence [1, 1, 2, 3, 4, 5, 8, 15, 50]. Eric Angelini calls these numbers, {2, 3, 4, 5, 8, 15, 50}, "Biprimes of K = A026242".
%H A247461 E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2014-September/013637.html">Biprimes of K</a>, Sep 17 2014
%o A247461 (PARI) /* first compute A026242 to a sufficient number of terms, then: */ for(k=3,#K=A026242, K[k] && forstep(i=k+K[k],#K,K[k],K[i]=0)); A247461=select(x->x,K)
%o A247461 /* to apply the stronger sieve */ for(k=3,#K=A026242, forstep(i=k+A026242[k],#K,A026242[k],K[i]=0)); select(x->x,K)
%K A247461 nonn
%O A247461 1,3
%A A247461 _M. F. Hasler_ and _Eric Angelini_, Sep 17 2014