cp's OEIS Frontend

A331869 Numbers n for which R(n) + 4*10^floor(n/2) is prime, where R(n) = (10^n-1)/9 (repunit: A002275).

%I A331869 #17 Apr 11 2023 07:17:33
%S A331869 1,3,4,15,76,91,231,1363,1714,1942,2497,4963,5379,12397,23224,26395
%N A331869 Numbers n for which R(n) + 4*10^floor(n/2) is prime, where R(n) = (10^n-1)/9 (repunit: A002275).
%C A331869 For n > 1, the corresponding primes are a subset of A105992: near-repunit primes.
%C A331869 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.
%C A331869 See also the variant A331868 where the digit 5 is just to the right of the middle.
%H A331869 Brady Haran and Simon Pampena, <a href="https://www.youtube.com/watch?v=HPfAnX5blO0">Glitch Primes and Cyclops Numbers</a>, Numberphile video (2015).
%e A331869 For n = 1, R(1) + 4*10^floor(1/2) = 5 is prime.
%e A331869 For n = 3, R(3) + 4*10^floor(3/2) = 151 is prime.
%e A331869 For n = 4, R(4) + 4*10^floor(4/2) = 1511 is prime.
%e A331869 For n = 15, R(15) + 4*10^floor(15/2) = 111111151111111 is prime.
%t A331869 Select[Range[0, 2500], PrimeQ[(10^# - 1)/9 + 4*10^Floor[#/2]] &]
%o A331869 (PARI) for(n=0,9999,ispseudoprime(p=10^n\9+4*10^(n\2))&&print1(n","))
%Y A331869 Cf. A105992 (near-repunit primes), A002275 (repunits), A004023 (indices of prime repunits), A011557 (powers of 10).
%Y A331869 Cf. A331862, A331861, A331865, A331866 (variants with digit 0, 2, 3 or 4 instead of 5), A331868 (variant with floor(n/2-1) instead of floor(n/2)).
%Y A331869 Cf. A077783 (odd terms).
%K A331869 nonn,base,hard,more
%O A331869 1,2
%A A331869 _M. F. Hasler_, Feb 09 2020
%E A331869 a(12)-a(14) from _Michael S. Branicky_, Feb 03 2023
%E A331869 a(15)-a(16) from _Michael S. Branicky_, Apr 11 2023