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A301617 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 1. 1
1, 19, 37, 73, 91, 109, 127, 163, 181, 199, 217, 253, 271, 289, 307, 343, 361, 379, 397, 433, 451, 469, 487, 523, 541, 559, 577, 613, 631, 649, 667, 703, 721, 739, 757, 793, 811, 829, 847, 883, 901, 919, 937, 973, 991, 1009, 1027, 1063, 1081, 1099 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers == {1, 19, 37, 73} mod 90 with additive sum sequence 1{+18+18+36+18} {repeat ...}. Includes all prime numbers > 7 with digital root 1.

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

n == {1, 19, 37, 73} mod 90.

a(n + 1) = a(n) + 18 * A177704(n + 1). - David A. Corneth, Mar 24 2018

From Colin Barker, Mar 24 2018: (Start)

G.f.: x*(1 + 18*x + 18*x^2 + 36*x^3 + 17*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

1+18=19; 19+18=37; 37+36=73; 73+18=91; 91+18=109.

MAPLE

seq(seq(i+90*j, i=[1, 19, 37, 73]), j=0..30); # Robert Israel, Mar 25 2018

MATHEMATICA

LinearRecurrence[{1, 0, 0, 1, -1}, {1, 19, 37, 73, 91}, 50] (* Harvey P. Dale, Dec 14 2019 *)

PROG

(PARI) a(n) = 1 + 18 * (n - 1 + n\4) \\ David A. Corneth, Mar 24 2018

(PARI) Vec(x*(1 + 18*x + 18*x^2 + 36*x^3 + 17*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Mar 24 2018

CROSSREFS

Cf. A177704, A045572.

Intersection of A007775 and A017173.

Sequence in context: A039321 A043144 A043924 * A211821 A061237 A158293

Adjacent sequences:  A301614 A301615 A301616 * A301618 A301619 A301620

KEYWORD

nonn,base,easy

AUTHOR

Gary Croft, Mar 24 2018

EXTENSIONS

The missing term 1081 added to the sequence by Colin Barker, Mar 24 2018

STATUS

approved

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Last modified October 30 20:11 EDT 2020. Contains 338090 sequences. (Running on oeis4.)