A301621 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 2.

11, 29, 47, 83, 101, 119, 137, 173, 191, 209, 227, 263, 281, 299, 317, 353, 371, 389, 407, 443, 461, 479, 497, 533, 551, 569, 587, 623, 641, 659, 677, 713, 731, 749, 767, 803, 821, 839, 857, 893, 911, 929, 947, 983, 1001, 1019, 1037, 1073, 1091, 1109

Offset

1,1

Comments

Numbers congruent to 11, 29, 47, or 83 mod 90 with additive sum sequence 11 { + 18 + 18 + 36 + 18} {repeat ...}. Includes all prime numbers greater than 5 with digital root 2.

Links

Table of n, a(n) for n=1..50.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 1, -1).

Formula

n == {11, 29, 47, 83} mod 90.

From Colin Barker, Mar 26 2018: (Start)

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

11+18=29; 29+18=47; 47+36=83; 83+18=101; 101+18=119.

Mathematica

Flatten[Table[90n - {79, 61, 43, 7}, {n, 30}]] (* Alonso del Arte, Mar 29 2018 *)

Prog

(PARI) Vec(x*(11 + 18*x + 18*x^2 + 36*x^3 + 7*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Mar 26 2018
(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)=2); # Muniru A Asiru, Apr 22 2018

Crossrefs

Intersection of A007775 and A017185.

Sequence in context: A249436 A167521 A031338 * A049229 A282538 A236485

Adjacent sequences: A301618 A301619 A301620 * A301622 A301623 A301624

Keyword

nonn,base,easy

Author

Gary Croft, Mar 24 2018

Status

approved