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A051884 Smallest number larger than the previous term which is not a prime but is relatively prime to the previous term.

%I A051884 #29 Jul 02 2025 16:01:58
%S A051884 1,4,9,10,21,22,25,26,27,28,33,34,35,36,49,50,51,52,55,56,57,58,63,64,
%T A051884 65,66,85,86,87,88,91,92,93,94,95,96,115,116,117,118,119,120,121,122,
%U A051884 123,124,125,126,143,144,145,146,147,148,153,154,155,156,161,162,169
%N A051884 Smallest number larger than the previous term which is not a prime but is relatively prime to the previous term.
%H A051884 T. D. Noe, <a href="/A051884/b051884.txt">Table of n, a(n) for n=1..1000</a>
%H A051884 A. Murthy, <a href="http://www.gallup.unm.edu/~smarandache/SN/ScArt5/ExploringNewIdeas.pdf">Exploring some new ideas on Smarandache type sets, functions and sequences</a>, Smarandache Notions Journal Vol. 11 N. 1-2-3 Spring 2000.
%p A051884 with(numtheory); i:=4; k:=5; while(k < 100) do while(order(k, i) = FAIL or isprime(k)) do k:=k+1; end do; print(k); i:= k; k:=k+1; end do; # _Ben Paul Thurston_, Feb 08 2007
%t A051884 rPrimeNext[n_]:=Module[{k},k=n+1;While[PrimeQ[k]||GCD[n,k]!=1,k++ ];k]; a=1;lst={a};Do[AppendTo[lst,a=rPrimeNext[a]],{n,0,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, May 15 2010 *)
%t A051884 nxt[n_]:=Module[{k=n+1},While[PrimeQ[k]||!CoprimeQ[k,n],k++];k]; NestList[ nxt,1,60] (* _Harvey P. Dale_, Mar 12 2013 *)
%o A051884 (Haskell)
%o A051884 a051884 n = a051884_list !! (n-1)
%o A051884 a051884_list =  1 : f 1 a002808_list where
%o A051884    f x cs = y : f y (dropWhile (<= y) cs) where
%o A051884      y = head [z | z <- cs, x `gcd` z == 1]
%o A051884 -- _Reinhard Zumkeller_, Jun 03 2013
%Y A051884 Sequences with related definitions: A072525, A085084, A126638, A131368, A163643.
%Y A051884 Cf. A002808.
%K A051884 nonn,nice,easy
%O A051884 1,2
%A A051884 _Felice Russo_, Dec 15 1999
%E A051884 More terms from _James Sellers_, Dec 16 1999
%E A051884 Definition corrected by _Franklin T. Adams-Watters_, Sep 19 2006