A135167 a(n) = 7^n + 5^n + 3^n - 2^n. Constants are the prime numbers in decreasing order.

2, 13, 79, 487, 3091, 20143, 133939, 903727, 6161731, 42325903, 292298899, 2026329967, 14085955171, 98111299663, 684331355059, 4778093404207, 33385561441411, 233393582449423, 1632228682334419, 11417969833438447, 79887637214988451, 559022711699743183, 3912205265750868979

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (17,-101,247,-210).

Formula

a(n) = 7^n + 5^n + 3^n - 2^n.

From G. C. Greubel, Sep 30 2016: (Start)

a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4).

G.f.: (2 - 21*x + 60*x^2 - 37*x^3)/((1 -2*x)*(1 -3*x)*(1 -5*x)*(1 -7*x)).

E.g.f.: exp(7*x) + exp(5*x) + exp(3*x) - exp(2*x). (End)

Example

a(4)=3091 because 7^4=2401, 5^4=625, 3^4=81, 2^4=16 and we can write 2401+625+81-16=3091.

Mathematica

Table[7^n + 5^n + 3^n - 2^n, {n, 0, 50}] (* or *) LinearRecurrence[{17, -101, 247, -210}, {2, 13, 79, 487}, 50] (* G. C. Greubel, Sep 30 2016 *)

Prog

(Magma) [7^n+5^n+3^n-2^n: n in [0..50]]; // Vincenzo Librandi, Dec 15 2010
(PARI) a(n)=7^n+5^n+3^n-2^n \\ Charles R Greathouse IV, Sep 30 2016

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.

Sequence in context: A212390 A198849 A037555 * A271475 A037491 A037571

Adjacent sequences: A135164 A135165 A135166 * A135168 A135169 A135170

Keyword

easy,nonn

Author

Omar E. Pol, Nov 21 2007

Extensions

More terms from Vincenzo Librandi, Dec 15 2010

Status

approved