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A291215 Numbers m with the property that shifting the rightmost digit of m to the left end multiplies the number by 7. 6
1014492753623188405797, 1159420289855072463768, 1304347826086956521739, 10144927536231884057971014492753623188405797, 11594202898550724637681159420289855072463768, 13043478260869565217391304347826086956521739, 101449275362318840579710144927536231884057971014492753623188405797 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

x = (10^21 - 7)/69 = 14492753623188405797.

a(1) = 7*x*10 + 7, a(2) = 8*x*10 + 8, a(3) = 9*x*10 + 9.

LINKS

Robert Israel, Table of n, a(n) for n = 1..135

Wikipedia, Parasitic number.

FORMULA

From Robert Israel, Aug 22 2017: (Start)

a(3k-2) = 7(10^(22k)-1)/69.

a(3k-1) = 8(10^(22k)-1)/69.

a(3k) = 9(10^(22k)-1)/69.

a(n+6) = (10^22+1) a(n+3) - 10^22 a(n).

G.f.: (1304347826086956521739*x^2 + 1159420289855072463768*x + 1014492753623188405797)/

(10^22*x^6 - (10^22+1)*x^3 + 1). (End)

EXAMPLE

b = 101449275362318840579.

a(1) = b*10 + 7,

7*a(1) = 7101449275362318840579 = 7*10^21 + b.

MAPLE

seq(seq(y*((10^(22*k)-1)/69), y=7..9), k=1..6); # Robert Israel, Aug 22 2017

CROSSREFS

Cf. A146088 (k=2), A146561 (k=3), A146569 (k=4), A146754 (k=5).

Cf. A092697, A097717.

Sequence in context: A181791 A217431 A173471 * A115541 A172564 A095438

Adjacent sequences:  A291212 A291213 A291214 * A291216 A291217 A291218

KEYWORD

nonn,base

AUTHOR

Seiichi Manyama, Aug 21 2017

STATUS

approved

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Last modified August 23 22:45 EDT 2019. Contains 326254 sequences. (Running on oeis4.)