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%I #42 May 11 2023 09:27:16
%S 10,16,22,28,36,40,46,52,58,66,70,78,82,88,96,100,106,112,126,130,136,
%T 148,156,162,166,172,178,190,196,210,222,226,232,238,250,256,262,268,
%U 276,280,292,306,310,316,330,336,346,352,358,366,372,378,382,388,396
%N Last term in a sequence of at least 3 consecutive composite integers.
%C An equivalent definition is "Last term in a sequence of at least 2 consecutive composite integers". - _Jon E. Schoenfield_, Dec 04 2017
%C The BASIC program below is useful in testing Grimm's Conjecture, subject of Carlos Rivera's Puzzle 430
%C Use the program with lines 30 and 70 enabled in the first run and then disabled with lines 31 and 71 enabled in the second run.
%C Composite numbers m such that m-1 is composite, and m+1 is not. - _Martin Michael Musatov_, Oct 24 2017
%H Michael De Vlieger, <a href="/A136799/b136799.txt">Table of n, a(n) for n = 1..10000</a>
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_430.htm">Puzzle 430, Grimm's Conjecture</a>, Prime puzzles and problems connection.
%F a(n) = A025584(n+2) - 1. - _R. J. Mathar_, Jan 24 2008
%F a(n) ~ n log n. - _Charles R Greathouse IV_, Oct 27 2015
%e a(1)=10 because 10 is the last term in a run of three composites beginning with 8 and ending with 10 (8,9,10).
%t Select[Prime@ Range@ 78, CompositeQ[# - 2] &] - 1 (* _Michael De Vlieger_, Oct 23 2015, after PARI *)
%o (UBASIC) 10 'puzzle 430 (gap finder) 20 N=1 30 A=1:S=sqrt(N):print N; 31 'A=1:S=N\2:print N; 40 B=N\A 50 if B*A=N and B=prmdiv(B) then print B; 60 A=A+1 70 if A<=sqrt(N) then 40 71 'if A<=N\2 then 40 80 C=C+1:print C 90 N=N+1: if N=prmdiv(N) then C=0:print:stop:goto 90:else 30
%o (PARI) forprime(p=5, 1000, if(isprime(p-2)==0, print1(p-1, ", "))) \\ _Altug Alkan_, Oct 23 2015
%o (Magma) [p-1: p in PrimesInInterval(4, 420) | not IsPrime(p - 2)]; // _Vincenzo Librandi_, Apr 11 2019
%Y Cf. A136798, A136800, A136801.
%K easy,nonn
%O 1,1
%A _Enoch Haga_, Jan 21 2008
%E Edited by _R. J. Mathar_, May 27 2009
%E a(53) corrected by _Bill McEachen_, Oct 27 2015
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