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A332117
a(n) = (10^(2n+1)-1)/9 + 6*10^n.
7
7, 171, 11711, 1117111, 111171111, 11111711111, 1111117111111, 111111171111111, 11111111711111111, 1111111117111111111, 111111111171111111111, 11111111111711111111111, 1111111111117111111111111, 111111111111171111111111111, 11111111111111711111111111111, 1111111111111117111111111111111
OFFSET
0,1
COMMENTS
See A107127 = {0, 3, 33, 311, 2933, ...} for the indices of primes.
LINKS
Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).
Patrick De Geest, Palindromic Wing Primes: (1)7(1), updated: June 25, 2017.
Makoto Kamada, Factorization of 11...11711...11, updated Dec 11 2018.
FORMULA
a(n) = A138148(n) + 7*10^n = A002275(2n+1) + 6*10^n.
G.f.: (7 - 606*x + 500*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
A332117 := n -> (10^(2*n+1)-1)/9+6*10^n;
MATHEMATICA
Array[(10^(2 # + 1)-1)/9 + 6*10^# &, 15, 0]
PROG
(PARI) apply( {A332117(n)=10^(n*2+1)\9+6*10^n}, [0..15])
(Python) def A332117(n): return 10**(n*2+1)//9+6*10**n
CROSSREFS
Cf. (A077789-1)/2 = A107127: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332127 .. A332197 (variants with different repeated digit 2, ..., 9).
Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).
Sequence in context: A178019 A337676 A266306 * A226598 A075599 A012500
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved