A295869 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 8.

17, 53, 71, 89, 107, 143, 161, 179, 197, 233, 251, 269, 287, 323, 341, 359, 377, 413, 431, 449, 467, 503, 521, 539, 557, 593, 611, 629, 647, 683, 701, 719, 737, 773, 791, 809, 827, 863, 881, 899, 917, 953, 971, 989, 1007, 1043, 1061, 1079, 1097, 1133

Offset: 1

Author

Gary Croft, Mar 24 2018

Keywords

• nonn
• base
• easy

Comments

Numbers == {17, 53, 71, 89} mod 90 with additive sum sequence 17{+36+18+18+18} {repeat ...}. Includes all prime numbers >5 with digital root 8.

Examples

			17+36=53; 53+18=71; 71+18=89; 89+18=107; 107+36=143.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Intersection of A007775 and A017257.

Programs

GAP

Filtered([1..1200],n->n mod 2<>0 and n mod 3 <>0 and n mod 5<>0 and n-9*Int((n-1)/9)=8); # Muniru A Asiru, May 30 2018

Maple

select(n->modp(n,2)<>0 and modp(n,3)<>0 and modp(n,5)<>0 and n-9*floor((n-1)/9)=8,[$1..1200]); # Muniru A Asiru, May 30 2018

PARI

Vec(x*(17 + 36*x + 18*x^2 + 18*x^3 + x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Mar 26 2018

Formula

Numbers == {17, 53, 71, 89} mod 90.

From Colin Barker, Mar 26 2018: (Start)

G.f.: x*(17 + 36*x + 18*x^2 + 18*x^3 + x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).

a(n) = (5 + 9*(-1)^n - (9+9*i)*(-i)^n - (9-9*i)*i^n + 90*n) / 4, where i=sqrt(-1).

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

(End)