A256619 - OEIS

%I #13 Sep 08 2022 08:46:11

%S 1,26,29,38,47,97,114,127,216,276,433,1094,1284

%N Numbers n such that there are no primes in the interval [b(n), b(n+1) - 1], where b(n) = 1 + Sum_{k=1..n} floor(1/2 + sqrt(2*k - 2)).

%C Numbers n such that there are no primes in the interval [A075349(n), A060432(n)].

%C Conjecture: the sequence is finite and complete.

%e 1st row:  {1}              - no prime!

%e 2nd row:  {2, 3}           - two primes (2 and 3).

%e 3rd row:  {4, 5}           - one prime (5).

%e 4th row:  {6, 7, 8}        - one prime (7).

%e 5th row:  {9, 10, 11}      - one prime (11).

%e 6th row:  {12, 13, 14}     - one prime (13).

%e 7th row:  {15, 16, 17, 18} - one prime (17).

%e 8th row:  {19, 20, 21, 22} - one prime (19).

%e 9th row:  {23, 24, 25, 26} - one prime (23).

%e 10th row: {27, 28, 29, 30} - one prime (29).

%e ...

%e 26th row: {120, 121, 122, 123, 124, 125, 126} - no primes!

%e ...

%e 29th row: {141, 142, 143, 144, 145, 146, 147, 148} - no primes!

%e ...

%o (Magma) lst:=[]; k:=1284; b:=1; e:=0; for n in [1..k] do b:=b+Floor(1/2+Sqrt(2*n-2)); e:=e+Floor(1/2+Sqrt(2*n)); if IsZero(#[m: m in [b..e] | IsPrime(m)]) then Append(~lst, n); end if; end for; lst;

%K nonn

%O 1,2

%A _Arkadiusz Wesolowski_, Apr 05 2015