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A332173
a(n) = 7*(10^(2n+1)-1)/9 - 4*10^n.
1
3, 737, 77377, 7773777, 777737777, 77777377777, 7777773777777, 777777737777777, 77777777377777777, 7777777773777777777, 777777777737777777777, 77777777777377777777777, 7777777777773777777777777, 777777777777737777777777777, 77777777777777377777777777777, 7777777777777773777777777777777
OFFSET
0,1
COMMENTS
According to M. Kamada, n = 0 and n = 2 are the only indices of a prime up to n = 2*10^4.
FORMULA
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.
MAPLE
A332173 := n -> 7*(10^(n*2+1)-1)/9 - 4*10^n;
MATHEMATICA
Array[7 (10^(2 # + 1) - 1)/9 - 4*10^# &, 15, 0]
PROG
(PARI) apply( {A332173(n)=10^(n*2+1)\9*7-4*10^n}, [0..15])
(Python) def A332173(n): return 10**(n*2+1)//9*7-4*10^n
CROSSREFS
Cf. A138148 (cyclops numbers with binary digits only).
Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).
Sequence in context: A255012 A133014 A100407 * A119264 A307926 A172895
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 06 2020
STATUS
approved