A123111 1+n^2+n^3+n^5+n^7; 10101101 in base n.

5, 173, 2467, 17489, 81401, 287965, 840743, 2130497, 4842829, 10101101, 19649675, 36082513, 63122177, 105954269, 171622351, 269488385, 411763733, 614115757, 896355059, 1283208401, 1805182345, 2499522653, 3411274487, 4594448449

Offset: 1

Author

Jonathan Vos Post, Sep 28 2006

Keywords

• easy
• nonn

Comments

4th row, A(4,n), of the infinite array A(k,n) = 1 + SUM[i=1..k]n^prime(i). If we deem prime(0) = 1, the array is A(k,n) = SUM[i=0..k]n^prime(i). The first row is A002522 = 1 + n^2. The second row is A098547 = 1 + n^2 + n^3. Row 4 (the current sequence) is prime for n = 1, 2, 3, 4, 5, 7, 10, 18, 19, 23, 25.

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A000040, A002522, A098547.

Programs

Maple

seq(1 + n^2 + n^3 + n^5 + n^7, n=1..100); # Robert Israel, Sep 02 2014

Mathematica

Table[Total[n^Prime[Range[4]]]+1,{n,30}] (* Harvey P. Dale, Jan 01 2014 *)

PARI

Vec(-x*(x^7-9*x^6-127*x^5-1227*x^4-2317*x^3-1223*x^2-133*x-5)/(x-1)^8 + O(x^100)) \\ Colin Barker, Sep 02 2014

Formula

a(n) = 1 + n^2 + n^3 + n^5 + n^7 = 10101101 (base n) = 1 + SUM[i=1..4]n^prime(i).

G.f.: -x*(x^7-9*x^6-127*x^5-1227*x^4-2317*x^3-1223*x^2-133*x-5) / (x-1)^8. - Colin Barker, Sep 02 2014

a(n+7)-7*a(n+6)+21*a(n+5)-35*a(n+4)+35*a(n+3)-21*a(n+2)+7*a(n+1)-a(n)=5040. - Robert Israel, Sep 02 2014