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 A262389 Numbers whose last digit is composite. 3
 4, 6, 8, 9, 14, 16, 18, 19, 24, 26, 28, 29, 34, 36, 38, 39, 44, 46, 48, 49, 54, 56, 58, 59, 64, 66, 68, 69, 74, 76, 78, 79, 84, 86, 88, 89, 94, 96, 98, 99, 104, 106, 108, 109, 114, 116, 118, 119, 124, 126, 128, 129, 134, 136, 138, 139, 144, 146, 148, 149 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers ending in 4, 6, 8 or 9. Union of A017317, A017341, A017365 and A017377. Subsequence of A118951 (numbers containing at least one composite digit). Complement of (A197652 Union A260181). LINKS Table of n, a(n) for n=1..60. Gerald Hillier and Didier Lachieze, Last Digit Composite. Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA G.f.: x*(4+2*x+2*x^2+x^3+x^4)/((x-1)^2*(1+x+x^2+x^3)). a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. a(n) = (5*n+1-(-1)^n+(3+(-1)^n)*(-1)^((2*n-3-(-1)^n)/4)/2)/2. Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(10-2*sqrt(5))*Pi - sqrt(5)*arccoth(3/sqrt(5)) - 4*log(2))/20. - Amiram Eldar, Jul 30 2024 MAPLE A262389:=n->(5*n+1-(-1)^n+(3+(-1)^n)*(-1)^((2*n-3-(-1)^n)/4)/2)/2: seq(A262389(n), n=1..100); MATHEMATICA Table[(5n+1-(-1)^n+(3+(-1)^n)*(-1)^((2n-3-(-1)^n)/4)/2)/2, {n, 100}] LinearRecurrence[{1, 0, 0, 1, -1}, {4, 6, 8, 9, 14}, 80] (* Vincenzo Librandi, Sep 21 2015 *) CoefficientList[Series[(4 + 2*x + 2*x^2 + x^3 + x^4)/((x - 1)^2*(1 + x + x^2 + x^3)), {x, 0, 80}], x] (* Wesley Ivan Hurt, Sep 21 2015 *) Select[Range[200], CompositeQ[Mod[#, 10]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 21 2019 *) PROG (Magma) [(5*n+1-(-1)^n+(3+(-1)^n)*(-1)^((2*n-3-(-1)^n) div 4) div 2) div 2: n in [1..70]]; // Vincenzo Librandi, Sep 21 2015 CROSSREFS Cf. A017317, A017341, A017365, A017377. Cf. A118951, A197652, A260181 (last digit is prime). Sequence in context: A119492 A285586 A118951 * A254755 A275624 A228019 Adjacent sequences: A262386 A262387 A262388 * A262390 A262391 A262392 KEYWORD nonn,base,easy AUTHOR Wesley Ivan Hurt, Sep 21 2015 EXTENSIONS Name edited by Jon E. Schoenfield, Feb 15 2018 STATUS approved

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Last modified September 17 14:32 EDT 2024. Contains 375987 sequences. (Running on oeis4.)