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 A317633 Numbers congruent to {1, 7, 9} mod 10. 3
 1, 7, 9, 11, 17, 19, 21, 27, 29, 31, 37, 39, 41, 47, 49, 51, 57, 59, 61, 67, 69, 71, 77, 79, 81, 87, 89, 91, 97, 99, 101, 107, 109, 111, 117, 119, 121, 127, 129, 131, 137, 139, 141, 147, 149, 151, 157, 159, 161, 167, 169 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS When multiplied by 10, one gets the numbers ending in "dix" in French (10, 70, 90, 110, ...). LINKS G. C. Greubel, Table of n, a(n) for n = 1..5000 Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1). FORMULA a(n) = a(n-3) + 10, a(1) = 1, a(2) = 7, a(3) = 9. From Bruno Berselli, Jul 02 2018: (Start) G.f.: x*(1 + 6*x + 2*x^2 + x^3)/((1 - x)^2*(1 + x + x^2)). a(n) = 2*n + 4*floor((n+1)/3) - 1. (End) EXAMPLE G.f. = x + 7*x^2 + 9*x^3+ 11*x^4 + 17*x^5 + 19*x^6 + 21*x^7 + 27*x^8 + ... - Michael Somos, Aug 19 2018 MATHEMATICA Table[2 n + 4 Floor[(n + 1)/3] - 1, {n, 1, 60}] (* Bruno Berselli, Jul 02 2018 *) Select[Range[0, 250], MemberQ[{1, 7, 9}, Mod[#, 10]]&] (* Vincenzo Librandi, Aug 05 2018 *) CoefficientList[ Series[(x^3 + 2x^2 + 6x + 1)/((x - 1)^2 (x^2 + x + 1)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 0, 1, -1}, {1, 7, 9, 11}, 61] (* Robert G. Wilson v, Aug 08 2018 *) PROG (MAGMA) [n: n in [0..170]|n mod 10 in {1, 7, 9}]; // Vincenzo Librandi, Aug 05 2018 (PARI) x='x+O('x^60); Vec(x*(1+6*x+2*x^2+x^3)/((1-x)^2*(1+x+x^2))) \\ G. C. Greubel, Aug 08 2018 CROSSREFS Cf. A008592, A010692. Sequence in context: A222947 A107226 A252663 * A259045 A029611 A053357 Adjacent sequences:  A317630 A317631 A317632 * A317634 A317635 A317636 KEYWORD nonn,easy AUTHOR Paul Curtz, Aug 02 2018 EXTENSIONS Definition from Jianing Song, Aug 02 2018 STATUS approved

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Last modified September 23 04:54 EDT 2020. Contains 337295 sequences. (Running on oeis4.)