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A301628 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 7. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 10 20:38 EST 2019. Contains 329909 sequences. (Running on oeis4.)