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A295869 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 8. 1
17, 53, 71, 89, 107, 143, 161, 179, 197, 233, 251, 269, 287, 323, 341, 359, 377, 413, 431, 449, 467, 503, 521, 539, 557, 593, 611, 629, 647, 683, 701, 719, 737, 773, 791, 809, 827, 863, 881, 899, 917, 953, 971, 989, 1007, 1043, 1061, 1079, 1097, 1133 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers == {17, 53, 71, 89} mod 90 with additive sum sequence 17{+36+18+18+18} {repeat ...}. Includes all prime numbers >5 with digital root 8.

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 == {17, 53, 71, 89} mod 90.

From Colin Barker, Mar 26 2018: (Start)

G.f.: x*(17 + 36*x + 18*x^2 + 18*x^3 + x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).

a(n) = (5 + 9*(-1)^n - (9+9*i)*(-i)^n - (9-9*i)*i^n + 90*n) / 4, where i=sqrt(-1).

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

(End)

EXAMPLE

17+36=53; 53+18=71; 71+18=89; 89+18=107; 107+36=143.

MAPLE

select(n->modp(n, 2)<>0 and modp(n, 3)<>0 and modp(n, 5)<>0 and n-9*floor((n-1)/9)=8, [$1..1200]); # Muniru A Asiru, May 30 2018

PROG

(PARI) Vec(x*(17 + 36*x + 18*x^2 + 18*x^3 + x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Mar 26 2018

(GAP) Filtered([1..1200], n->n mod 2<>0 and n mod 3 <>0 and n mod 5<>0 and n-9*Int((n-1)/9)=8); # Muniru A Asiru, May 30 2018

CROSSREFS

Intersection of A007775 and A017257.

Sequence in context: A286211 A213997 A062342 * A061242 A062343 A176254

Adjacent sequences:  A295866 A295867 A295868 * A295870 A295871 A295872

KEYWORD

nonn,base,easy

AUTHOR

Gary Croft, Mar 24 2018

STATUS

approved

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Last modified August 15 01:28 EDT 2020. Contains 336484 sequences. (Running on oeis4.)