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 A221855 Number of cyclotomic cosets of 13 mod 10^n. 1
 4, 12, 30, 72, 130, 204, 294, 400, 522, 660, 814, 984, 1170, 1372, 1590, 1824, 2074, 2340, 2622, 2920, 3234, 3564, 3910, 4272, 4650, 5044, 5454, 5880, 6322, 6780, 7254, 7744, 8250, 8772, 9310, 9864, 10434, 11020, 11622, 12240, 12874, 13524, 14190, 14872, 15570, 16284, 17014, 17760, 18522, 19300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS FORMULA a(n) = A220018(n) for n = 1. a(n) = A220018(n) + 1 for all n >= 2. Conjecture: a(n) = 2*n*(4*n-7) for n>2. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>5. G.f.: 2*x*(4*x^4-7*x^3-3*x^2-2) / (x-1)^3. - Colin Barker, Apr 14 2013 EXAMPLE a(2) = 12 because there are 12 cyclotomic cosets of 13 mod 100: {1, 13, 69, 97, 61, 93, 9, 17, 21, 73, 49, 37, 81, 53, 89, 57, 41, 33, 29, 77} {3, 39, 7, 91, 83, 79, 27, 51, 63, 19, 47, 11, 43, 59, 67, 71, 23, 99, 87, 31} {2, 26, 38, 94, 22, 86, 18, 34, 42, 46, 98, 74, 62, 6, 78, 14, 82, 66, 58, 54} {4, 52, 76, 88, 44, 72, 36, 68, 84, 92, 96, 48, 24, 12, 56, 28, 64, 32, 16, 8} {5, 65, 45, 85} {15, 95, 35, 55} {25} {75} {10, 30, 90, 70} {20, 60, 80, 40} {50} {0} PROG (PARI) for(n=1, 50, print1(sumdiv(10^n, d, eulerphi(d)/znorder(Mod(13, d)))", ")) CROSSREFS Cf. A006694, A220468. Sequence in context: A249914 A006802 A068055 * A258457 A279152 A317780 Adjacent sequences:  A221852 A221853 A221854 * A221856 A221857 A221858 KEYWORD base,nonn AUTHOR V. Raman, Jan 28 2013 STATUS approved

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Last modified July 22 05:47 EDT 2019. Contains 325213 sequences. (Running on oeis4.)