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

Author

Gary Croft, Mar 24 2018

Keywords

• nonn
• base
• easy

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.

Examples

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

Links

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

Crossrefs

Intersection of A007775 and A017185.

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)=2); # Muniru A Asiru, Apr 22 2018

Mathematica

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

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

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)