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 A005381 Numbers k such that k and k-1 are composite. (Formerly M4598) 45
 9, 10, 15, 16, 21, 22, 25, 26, 27, 28, 33, 34, 35, 36, 39, 40, 45, 46, 49, 50, 51, 52, 55, 56, 57, 58, 63, 64, 65, 66, 69, 70, 75, 76, 77, 78, 81, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 100, 105, 106, 111, 112, 115, 116, 117, 118, 119, 120, 121, 122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Position where the composites first outnumber the primes by n, among the first natural numbers. - Lekraj Beedassy, Jul 11 2006 REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS J. Stauduhar, Table of n, a(n) for n = 1..10000 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. R. P. Boas & N. J. A. Sloane, Correspondence, 1974 B. W. J. Irwin, Recursive Modular Conjecture for pi(n). FORMULA Conjecture: pi(n)=Sum_{k=1..n} k mod a(m) mod a(m-1) ... mod a(1) mod 2, for all values 12, isprime(n)=(n mod x) mod 2, where x is the largest a(n)<=n. - Benedict W. J. Irwin, May 06 2016 MAPLE isA005381 := proc(n) not isprime(n) and not isprime(n-1) ; end proc: A005381 := proc(n) local a; option remember; if n = 1 then 9; else for a from procname(n-1)+1 do if isA005381(a) then return a; end if; end do: end if; end proc: # R. J. Mathar, Jul 14 2015 # second Maple program: q:= n-> ormap(isprime, [n, n-1]): remove(q, [\$2..130])[]; # Alois P. Heinz, Dec 26 2021 MATHEMATICA Select[Range[2, 200], ! PrimeQ[# - 1] && ! PrimeQ[#] &] PROG (PARI) is(n)=!isprime(n)&&!isprime(n-1) \\ M. F. Hasler, Jan 07 2019 (Python) from sympy import isprime def ok(n): return n > 3 and not isprime(n) and not isprime(n-1) print([k for k in range(122) if ok(k)]) # Michael S. Branicky, Dec 26 2021 CROSSREFS Equals A068780 + 1. Cf. A007921. Cf. A093515 (complement, apart from 1 which is in neither sequence), A323162 (characteristic function). Sequence in context: A227943 A114844 A194593 * A175090 A365166 A197113 Adjacent sequences: A005378 A005379 A005380 * A005382 A005383 A005384 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified September 15 12:32 EDT 2024. Contains 375938 sequences. (Running on oeis4.)