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

1,1

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.

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 == {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)

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

Intersection of A007775 and A017221.

Sequence in context: A050668 A199219 A115699 * A163635 A376013 A083444

Adjacent sequences: A301620 A301621 A301622 * A301624 A301625 A301626

Keyword

nonn,base,easy

Author

Gary Croft, Mar 24 2018

Status

approved