A301622 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 4.

13, 31, 49, 67, 103, 121, 139, 157, 193, 211, 229, 247, 283, 301, 319, 337, 373, 391, 409, 427, 463, 481, 499, 517, 553, 571, 589, 607, 643, 661, 679, 697, 733, 751, 769, 787, 823, 841, 859, 877, 913, 931, 949, 967, 1003, 1021, 1039, 1057, 1093, 1111

Offset

1,1

Comments

Numbers == {13, 31, 49, 67} mod 90 with additive sum sequence 13{+18+18+18+36} {repeat ...}. Includes all prime numbers > 5 with digital root 4.

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 == {13, 31, 49, 67} mod 90.

From Colin Barker, Mar 25 2018: (Start)

G.f.: x*(13 + 18*x + 18*x^2 + 18*x^3 + 23*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)

Mathematica

Rest@ CoefficientList[Series[x (13 + 18 x + 18 x^2 + 18 x^3 + 23 x^4)/((1 - x)^2*(1 + x) (1 + x^2)), {x, 0, 50}], x] (* Michael De Vlieger, Apr 21 2018 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {13, 31, 49, 67, 103}, 50] (* Harvey P. Dale, May 11 2019 *)

Prog

(PARI) Vec(x*(13 + 18*x + 18*x^2 + 18*x^3 + 23*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Mar 25 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)=4); # Muniru A Asiru, Apr 22 2018

Crossrefs

Intersection of A007775 and A017209.

Sequence in context: A106294 A101649 A063305 * A166143 A065768 A155820

Adjacent sequences: A301619 A301620 A301621 * A301623 A301624 A301625

Keyword

nonn,base,easy

Author

Gary Croft, Mar 24 2018

Extensions

Last term corrected by Colin Barker, Mar 25 2018

Status

approved