A256619 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)).

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

Offset: 1

Author

Arkadiusz Wesolowski, Apr 05 2015

Keywords

• nonn

Comments

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

Conjecture: the sequence is finite and complete.

Examples

			1st row:  {1}              - no prime!
2nd row:  {2, 3}           - two primes (2 and 3).
3rd row:  {4, 5}           - one prime (5).
4th row:  {6, 7, 8}        - one prime (7).
5th row:  {9, 10, 11}      - one prime (11).
6th row:  {12, 13, 14}     - one prime (13).
7th row:  {15, 16, 17, 18} - one prime (17).
8th row:  {19, 20, 21, 22} - one prime (19).
9th row:  {23, 24, 25, 26} - one prime (23).
10th row: {27, 28, 29, 30} - one prime (29).
...
26th row: {120, 121, 122, 123, 124, 125, 126} - no primes!
...
29th row: {141, 142, 143, 144, 145, 146, 147, 148} - no primes!
...
		

Programs

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;