OFFSET
1,1
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.
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).
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)
EXAMPLE
17+36=53; 53+18=71; 71+18=89; 89+18=107; 107+36=143.
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
PROG
(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
(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
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Gary Croft, Mar 24 2018
STATUS
approved