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URL: https://oeis.org/A332118

⇱ A332118 - OEIS

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A332118
a(n) = (10^(2*n+1) - 1)/9 + 7*10^n.
7
8, 181, 11811, 1118111, 111181111, 11111811111, 1111118111111, 111111181111111, 11111111811111111, 1111111118111111111, 111111111181111111111, 11111111111811111111111, 1111111111118111111111111, 111111111111181111111111111, 11111111111111811111111111111, 1111111111111118111111111111111
OFFSET
0,1
COMMENTS
See A107648 = {1, 4, 6, 7, 384, 666, ...} for the indices of primes.
LINKS
Patrick De Geest, Palindromic Wing Primes: (1)8(1), updated: June 25, 2017.
Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).
Makoto Kamada, Factorization of 11...11811...11, updated Dec 11 2018.
FORMULA
a(n) = A138148(n) + 8*10^n = A002275(2*n+1) + 7*10^n.
G.f.: (8 - 707*x + 600*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.
E.g.f.: exp(x)*(10*exp(99*x) + 63*exp(9*x) - 1)/9. - Elmo R. Oliveira, Dec 16 2025
MAPLE
A332118 := n -> (10^(2*n+1)-1)/9+7*10^n;
MATHEMATICA
Array[(10^(2 # + 1)-1)/9 + 7*10^# &, 15, 0]
PROG
(PARI) apply( {A332118(n)=10^(n*2+1)\9+7*10^n}, [0..15])
(Python) def A332118(n): return 10**(n*2+1)//9+7*10**n
CROSSREFS
Cf. (A077791-1)/2 = A107648: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes), A077798 (palindromic wing primes), A088281 (primes 1..1x1..1), A068160 (smallest of given length), A053701 (vertically symmetric numbers).
Cf. A332128 .. A332178, A181965 (variants with different repeated digit 2, ..., 9).
Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).
Sequence in context: A374890 A060593 A130775 * A261825 A203359 A294355
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved