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A301622 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 4. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 10 20:38 EST 2019. Contains 329909 sequences. (Running on oeis4.)