A301628 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 7.

7, 43, 61, 79, 97, 133, 151, 169, 187, 223, 241, 259, 277, 313, 331, 349, 367, 403, 421, 439, 457, 493, 511, 529, 547, 583, 601, 619, 637, 673, 691, 709, 727, 763, 781, 799, 817, 853, 871, 889, 907, 943, 961, 979, 997, 1033, 1051, 1069, 1087, 1123

Offset

1,1

Comments

Numbers == {7, 43, 61, 79} mod 90 with additive sum sequence 7{+36+18+18+18} {repeat ...}. Includes all prime numbers > 5 with digital root 7.

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 == {7, 43, 61, 79} mod 90.

From Colin Barker, Sep 21 2019: (Start)

G.f.: x*(7 + 36*x + 18*x^2 + 18*x^3 + 11*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

7+36=43; 43+18=61; 61+18=79; 79+18=97; 97+36=133.

Prog

(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)=7); # Muniru A Asiru, Apr 22 2018
(PARI) Vec(x*(7 + 36*x + 18*x^2 + 18*x^3 + 11*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^40)) \\ Colin Barker, Sep 21 2019

Crossrefs

Intersection of A007775 and A017245.

Sequence in context: A062336 A085704 A243459 * A061241 A062337 A176252

Adjacent sequences: A301625 A301626 A301627 * A301629 A301630 A301631

Keyword

nonn,base,easy

Author

Gary Croft, Mar 24 2018

Status

approved