A136799 Last term in a sequence of at least 3 consecutive composite integers.

10, 16, 22, 28, 36, 40, 46, 52, 58, 66, 70, 78, 82, 88, 96, 100, 106, 112, 126, 130, 136, 148, 156, 162, 166, 172, 178, 190, 196, 210, 222, 226, 232, 238, 250, 256, 262, 268, 276, 280, 292, 306, 310, 316, 330, 336, 346, 352, 358, 366, 372, 378, 382, 388, 396

Offset

1,1

Comments

An equivalent definition is "Last term in a sequence of at least 2 consecutive composite integers". - Jon E. Schoenfield, Dec 04 2017

The BASIC program below is useful in testing Grimm's Conjecture, subject of Carlos Rivera's Puzzle 430

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.

Composite numbers m such that m-1 is composite, and m+1 is not. - Martin Michael Musatov, Oct 24 2017

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Carlos Rivera, Puzzle 430, Grimm's Conjecture, Prime puzzles and problems connection.

Formula

a(n) = A025584(n+2) - 1. - R. J. Mathar, Jan 24 2008

a(n) ~ n log n. - Charles R Greathouse IV, Oct 27 2015

Example

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).

Mathematica

Select[Prime@ Range@ 78, CompositeQ[# - 2] &] - 1 (* Michael De Vlieger, Oct 23 2015, after PARI *)

Prog

(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
(PARI) forprime(p=5, 1000, if(isprime(p-2)==0, print1(p-1, ", "))) \\ Altug Alkan, Oct 23 2015
(Magma) [p-1: p in PrimesInInterval(4, 420) | not IsPrime(p - 2)]; // Vincenzo Librandi, Apr 11 2019

Crossrefs

Cf. A136798, A136800, A136801.

Sequence in context: A242057 A245024 A264721 * A055987 A187397 A152138

Adjacent sequences: A136796 A136797 A136798 * A136800 A136801 A136802

Keyword

easy,nonn

Author

Enoch Haga, Jan 21 2008

Extensions

Edited by R. J. Mathar, May 27 2009

a(53) corrected by Bill McEachen, Oct 27 2015

Status

approved