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

Author

Gary Croft, Mar 24 2018

Keywords

• nonn
• base
• easy

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.

Examples

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

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 A017245.

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)=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

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)