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#10 by M. F. Hasler at Tue Feb 11 08:26:35 EST 2020
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#9 by M. F. Hasler at Tue Feb 11 08:26:15 EST 2020
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| MATHEMATICA
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Array[7 (10^(2 # + 1) - 1)/9 - 4*10^# &, 15, 0]
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| STATUS
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approved
editing
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#8 by M. F. Hasler at Sat Feb 08 18:03:23 EST 2020
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#7 by M. F. Hasler at Sat Feb 08 18:03:12 EST 2020
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#6 by M. F. Hasler at Sat Feb 08 18:02:10 EST 2020
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| PROG
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(Python) def A332173(n): return 10**(n*2+1)//9*7-4*10^n
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| CROSSREFS
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Cf. A002275 (repunits R_n = [10^n/9]), A002281 (7*R_n), A011557 (10^n).
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| STATUS
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approved
editing
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#5 by M. F. Hasler at Sat Feb 08 17:27:47 EST 2020
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#4 by M. F. Hasler at Sat Feb 08 17:27:20 EST 2020
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| CROSSREFS
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Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).
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#3 by M. F. Hasler at Sat Feb 08 14:36:03 EST 2020
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| MAPLE
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A332173 := n -> 7*(10^(n*2+1)-1)/9 - 4*10^n;
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| MATHEMATICA
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Array[7 (10^(2 # + 1) - 1)/9 - 4*10^# &, 15]
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#2 by M. F. Hasler at Sat Feb 08 14:33:21 EST 2020
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| NAME
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allocated for M. F. Hasler
a(n) = 7*(10^(2n+1)-1)/9 - 4*10^n.
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| DATA
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3, 737, 77377, 7773777, 777737777, 77777377777, 7777773777777, 777777737777777, 77777777377777777, 7777777773777777777, 777777777737777777777, 77777777777377777777777, 7777777777773777777777777, 777777777777737777777777777, 77777777777777377777777777777, 7777777777777773777777777777777
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| OFFSET
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0,1
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| COMMENTS
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According to M. Kamada, n = 0 and n = 2 are the only indices of a prime up to n = 2*10^4.
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| LINKS
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Makoto Kamada, <a href="https://stdkmd.net/nrr/7/77377.htm">Factorization of 77...77377...77</a>, updated Dec 11 2018.
<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
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| FORMULA
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a(n) = 7*A138148(n) + 3*10^n.
G.f.: (1 + 404*x - 1100*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>2.
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| PROG
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(PARI) apply( {A332173(n)=10^(n*2+1)\9*7-4*10^n}, [0..15])
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| CROSSREFS
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Cf. A138148 (cyclops numbers with binary digits only).
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| KEYWORD
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allocated
nonn,base,easy,changed
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| AUTHOR
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M. F. Hasler, Feb 06 2020
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| STATUS
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approved
editing
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#1 by M. F. Hasler at Thu Feb 06 20:55:20 EST 2020
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| NAME
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allocated for M. F. Hasler
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| KEYWORD
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allocated
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| STATUS
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approved
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