A301617 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 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

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