OFFSET
1,2
COMMENTS
For n > 1, the corresponding primes are a subset of A105992: near-repunit primes.
In base 10, R(n) + 4*10^floor(n/2) has ceiling(n/2)-1 digits 1, one digit 5, and again floor(n/2) digits 1, except for n = 0. For odd n, this is a palindrome (a.k.a. wing prime, cf. A077783: subsequence of odd terms), for even n the digit 5 is just left to the middle of the number.
See also the variant A331868 where the digit 5 is just to the right of the middle.
LINKS
Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).
EXAMPLE
For n = 1, R(1) + 4*10^floor(1/2) = 5 is prime.
For n = 3, R(3) + 4*10^floor(3/2) = 151 is prime.
For n = 4, R(4) + 4*10^floor(4/2) = 1511 is prime.
For n = 15, R(15) + 4*10^floor(15/2) = 111111151111111 is prime.
MATHEMATICA
Select[Range[0, 2500], PrimeQ[(10^# - 1)/9 + 4*10^Floor[#/2]] &]
PROG
(PARI) for(n=0, 9999, ispseudoprime(p=10^n\9+4*10^(n\2))&&print1(n", "))
CROSSREFS
KEYWORD
nonn,base,hard,more
AUTHOR
M. F. Hasler, Feb 09 2020
EXTENSIONS
a(12)-a(14) from Michael S. Branicky, Feb 03 2023
a(15)-a(16) from Michael S. Branicky, Apr 11 2023
STATUS
approved