A010484 -id:A010484 - cp's OEIS frontend

A177035 Decimal expansion of sqrt(13493990).

3, 6, 7, 3, 4, 1, 6, 6, 6, 5, 7, 2, 1, 4, 3, 7, 0, 5, 1, 3, 6, 6, 9, 3, 6, 1, 5, 1, 9, 2, 0, 9, 7, 7, 4, 5, 9, 8, 4, 5, 4, 1, 6, 4, 1, 0, 5, 9, 3, 4, 2, 3, 5, 3, 2, 4, 9, 6, 8, 0, 7, 4, 3, 0, 1, 6, 2, 4, 1, 9, 7, 3, 8, 8, 0, 7, 0, 9, 6, 9, 5, 4, 7, 0, 3, 5, 4, 9, 9, 2, 6, 8, 7, 7, 3, 9, 0, 7, 4, 2, 8, 7, 9, 9, 2

Offset: 4

Klaus Brockhaus, May 01 2010

Continued fraction expansion of sqrt(13493990) is 3673 followed by (repeat 2, 2, 2, 7346).

sqrt(13493990) = sqrt(2)*sqrt(5)*sqrt(19)*sqrt(29)*sqrt(31)*sqrt(79).

			sqrt(13493990) = 3673.41666572143705136693...

Cf. A002193 (decimal expansion of sqrt(2)), A002163 (decimal expansion of sqrt(5)), A010475 (decimal expansion of sqrt(19)), A010484 (decimal expansion of sqrt(29)), A010486 (decimal expansion of sqrt(31)), A010531 (decimal expansion of sqrt(79)), A177034 (decimal expansion of (9280+3*sqrt(13493990))/14165).

RealDigits[Sqrt[13493990],10,120][[1]] (* Harvey P. Dale, Nov 11 2016 *)

A367456 Expansion of (1 - x)/(1 - x - 7*x^2).

Original entry on oeis.org

1, 0, 7, 7, 56, 105, 497, 1232, 4711, 13335, 46312, 139657, 463841, 1441440, 4688327, 14778407, 47596696, 151045545, 484222417, 1541541232, 4931098151, 15721886775, 50239573832, 160292781257, 511969798081, 1634019266880, 5217807853447, 16655942721607, 53180597695736, 169772196746985

Offset: 0

Wolfdieter Lang, Jan 16 2024

a(n) appears in the formula for powers of the fundamental algebraic number c = (1 + sqrt(29))/2 = A223140 of the quadratic number field Q(sqrt(29)): c^n = a(n) + A015442(n), for n >= 0. The formulas given below and in A015442 in terms of S-Chebyshev polynomials are valid also for c^(-n), for n >= 0, with 1/c = (-1 + sqrt(29))/14 = A367454.

a(n) is the number of compositions (ordered partitions) of n into parts >= 2 and there are 7 sorts of each part. - Joerg Arndt, Jan 16 2024

Cf.: A010484, A015442 (partial sums), A049310, A223140, A367454.

LinearRecurrence[{1,7},{1,0},30] (* James C. McMahon, Jan 16 2024 *)

a(n) = a(n-1) + 7*a(n-2), with a(0) = 1, a(1) = 0.
G.f.: (1 - x)/(1 - x - 7*x^2).
a(n) = 7*A015442(n-1), with A015442(-1) = 1/7.
a(n) = 7*(-i*sqrt(7))^(n-2)*S(n-2, i/sqrt(7)), with i = sqrt(-1) and the S-Chebyshev polynomial (see A049310). S(-2, x) = -1 and S(-1, x) = 0. The Fibonacci polynomials are F(n, x) = (-i)^(n-1)*S(n-1, i*x).

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A177035 Decimal expansion of sqrt(13493990).

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