A301623 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 5.

23, 41, 59, 77, 113, 131, 149, 167, 203, 221, 239, 257, 293, 311, 329, 347, 383, 401, 419, 437, 473, 491, 509, 527, 563, 581, 599, 617, 653, 671, 689, 707, 743, 761, 779, 797, 833, 851, 869, 887, 923, 941, 959, 977, 1013, 1031, 1049, 1067, 1103, 1121

Offset: 1

Author

Gary Croft, Mar 24 2018

Keywords

• nonn
• base
• easy

Comments

Numbers == {23, 41, 59, 77} mod 90 with additive sum sequence 23{+18+18+18+36} {repeat ...}. Includes all primes number > 5 with digital root 5.

Examples

			23+18=41; 41+18=59; 59+18=77; 77+36=113; 113+18=131.
		

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 A017221.

Programs

GAP

Filtered(Filtered([1..1200],n->n mod 2 <> 0 and n mod 3 <> 0 and n mod 5 <> 0),i->i-9*Int((i-1)/9)=5); # Muniru A Asiru, Apr 22 2018

Mathematica

LinearRecurrence[{1,0,0,1,-1},{23,41,59,77,113},50] (* Harvey P. Dale, Jul 28 2018 *)

PARI

Vec(x*(23 + 18*x + 18*x^2 + 18*x^3 + 13*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Mar 25 2018

Formula

Numbers == {23, 41, 59, 77} mod 90.

From Colin Barker, Mar 25 2018: (Start)

G.f.: x*(23 + 18*x + 18*x^2 + 18*x^3 + 13*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).

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

(End)