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 A270346 a(n) is the number whose base-11 digits are, in order, the first n terms of the simple periodic sequence: repeat 2,3,5,7. 0
 2, 25, 280, 3087, 33959, 373552, 4109077, 45199854, 497198396, 5469182359, 60161005954, 661771065501, 7279481720513, 80074298925646, 880817288182111, 9688990170003228, 106578891870035510, 1172367810570390613, 12896045916274296748, 141856505079017264235 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The periodic sequence comprises the first four primes, and the selected base is the fifth prime. LINKS Index entries for linear recurrences with constant coefficients, signature (11,0,0,1,-11). FORMULA a(1)=2, a(2)=25, a(3)=280, a(4)=3087, a(5)=33959, a(n) = 11*a(n-1) + a(n-4) - 11*a(n-5). - Harvey P. Dale, Mar 15 2016 G.f.: x*(2+3*x+5*x^2+7*x^3) / ((1-x)*(1+x)*(1-11*x)*(1+x^2)). - Colin Barker, Jul 31 2016 EXAMPLE a(8) = 45199854 = 23572357_11. MATHEMATICA Table[FromDigits[PadRight[{}, n, {2, 3, 5, 7}], 11], {n, 30}] (* or *) LinearRecurrence[{11, 0, 0, 1, -11}, {2, 25, 280, 3087, 33959}, 31] PROG (PARI) a(n) = (-2074+305*(-1)^n+(370+410*I)*(-I)^n+(370-410*I)*I^n+1029*11^n)/4880 \\ Colin Barker, Jul 31 2016 (PARI) Vec(x*(2+3*x+5*x^2+7*x^3)/((1-x)*(1+x)*(1-11*x)*(1+x^2)) + O(x^30)) \\ Colin Barker, Jul 31 2016 (MAGMA) R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x*(2+3*x+5*x^2+7*x^3)/((1-x^4)*(1-11*x)) )); // G. C. Greubel, Jul 14 2019 (Sage) a=(x*(2+3*x+5*x^2+7*x^3)/((1-x^4)*(1-11*x))).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Jul 14 2019 (GAP) a:=[2, 25, 280, 3087, 33959];; for n in [6..30] do a[n]:=11*a[n-1]+a[n-4]-11*a[n-5]; od; a; # G. C. Greubel, Jul 14 2019 CROSSREFS Cf. A033113. Sequence in context: A174970 A249893 A085830 * A212022 A198710 A074209 Adjacent sequences:  A270343 A270344 A270345 * A270347 A270348 A270349 KEYWORD nonn,easy,base AUTHOR Harvey P. Dale, Mar 15 2016 STATUS approved

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Last modified June 25 20:02 EDT 2022. Contains 354851 sequences. (Running on oeis4.)