

A301623


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


1



23, 41, 59, 77, 113, 131, 149, 167, 203, 221, 239, 257, 293, 311, 329, 347, 383, 401, 419, 437, 473, 491, 509, 527, 563, 581, 599, 617, 653, 671, 689, 707, 743, 761, 779, 797, 833, 851, 869, 887, 923, 941, 959, 977, 1013, 1031, 1049, 1067, 1103, 1121
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OFFSET

1,1


COMMENTS

Numbers == {23, 41, 59, 77} mod 90 with additive sum sequence 23{+18+18+18+36} {repeat ...}. Includes all primes number > 5 with digital root 5.


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 == {23, 41, 59, 77} mod 90.
From Colin Barker, Mar 25 2018: (Start)
G.f.: x*(23 + 18*x + 18*x^2 + 18*x^3 + 13*x^4) / ((1  x)^2*(1 + x)*(1 + x^2)).
a(n) = a(n1) + a(n4)  a(n5) for n>5.
(End)


EXAMPLE

23+18=41; 41+18=59; 59+18=77; 77+36=113; 113+18=131.


MATHEMATICA

LinearRecurrence[{1, 0, 0, 1, 1}, {23, 41, 59, 77, 113}, 50] (* Harvey P. Dale, Jul 28 2018 *)


PROG

(PARI) Vec(x*(23 + 18*x + 18*x^2 + 18*x^3 + 13*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>i9*Int((i1)/9)=5); # Muniru A Asiru, Apr 22 2018


CROSSREFS

Intersection of A007775 and A017221.
Sequence in context: A050668 A199219 A115699 * A163635 A083444 A153037
Adjacent sequences: A301620 A301621 A301622 * A301624 A301625 A301626


KEYWORD

nonn,base,easy


AUTHOR

Gary Croft, Mar 24 2018


STATUS

approved



