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.

2, 25, 280, 3087, 33959, 373552, 4109077, 45199854, 497198396, 5469182359, 60161005954, 661771065501, 7279481720513, 80074298925646, 880817288182111, 9688990170003228, 106578891870035510, 1172367810570390613, 12896045916274296748, 141856505079017264235

Offset: 1

Author

Harvey P. Dale, Mar 15 2016

Keywords

• nonn
• easy
• base

Comments

The periodic sequence comprises the first four primes, and the selected base is the fifth prime.

Examples

			a(8) = 45199854 = 23572357_11.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (11,0,0,1,-11).

Crossrefs

Cf. A033113.

Programs

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

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

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]

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

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

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