Olivier Bélot - cp's OEIS frontend

User: Olivier Bélot

Olivier Bélot has authored 2 sequences.

A303214 Prime numbers whose average with the previous prime is not divisible by 2 or 3.

3, 211, 223, 479, 521, 631, 673, 809, 1009, 1213, 1249, 1319, 1471, 1511, 1523, 1543, 1693, 1721, 1801, 1823, 1901, 2081, 2111, 2203, 2309, 2411, 2459, 2591, 2633, 2789, 2939, 3061, 3079, 3181, 3203, 3271, 3343, 3359, 3511, 3571, 3671, 3943, 4001, 4091, 4111

Offset: 1

Olivier Bélot, Apr 19 2018

nonn

Very similar to A031931.

3 and all prime(k+1) such that A001223(k) is divisible by 12. - Robert Israel, Jul 04 2018

			p = 223 => (p + previous_prime(p))/2 = (223 +211)/2 = 7*31;
p =  53 => (p + previous_prime(p))/2 =  (53 + 51)/2 = 52 (divisible by 2).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001223, A031931.

count:= 1: Res:= 3:
p:= 3:
while count < 100 do
  q:= p; p:= nextprime(p);
  v:= (q+p)/2;
  if igcd(v,6)=1 then
    count:= count+1;
    Res:= Res, p;
  fi
od:
Res;# Robert Israel, Jul 04 2018

ok(n)={my(t=n+precprime(n-1)); n > 2 && isprime(n) && t%4 && t%3} \\ Andrew Howroyd, Jul 02 2018

2 NOT(|) (p+previous_prime(p))/2 AND 3 NOT(|) (p+previous_prime(p))/2

A281318 Number of consecutive nonprime numbers following Euclid numbers A006862.

Original entry on oeis.org

1, 3, 5, 11, 21, 15, 17, 21, 35, 59, 65, 59, 69, 45, 105, 57, 59, 107, 87, 101, 77, 149, 195, 99, 101, 231, 221, 125, 221, 189, 161, 227, 641, 237, 155, 165, 437, 237, 197, 189, 197, 381, 231, 749, 311, 771, 605, 311, 381, 291, 441, 329, 281, 275, 269, 399

Offset: 1

Olivier Bélot, Jan 20 2017

nonn

For n > 1, a(n) >= prime(n), with equality if and only if A006862(n) + prime(n) + 1 is prime. Equality occurs for n=2, 3, 7, 17. Are there any others? - Robert Israel, Jan 30 2017

			a(3) = 5 because primorial p_3# = 5# = 2*3*5 = 30 thus 31 is the third Euclid number, and there are 5 consecutive nonprime numbers {32,33,34,35,36} between 31 and the next prime, 37. - _Michael De Vlieger_, Jan 20 2017

Robert Israel, Table of n, a(n) for n = 1..469

Cf. A006862, A002110.

p:= 0: pn:= 1:
for n from 1 to 100 do
  p:= nextprime(p);
pn:= pn*p;
A[n]:= nextprime(pn+1)-(pn+2);
od:
seq(A[n],n=1..100); # Robert Israel, Jan 30 2017

Table[Function[p, NextPrime@ p - p - 1][Times @@ Prime@ Range@ n + 1], {n, 56}] (* Michael De Vlieger, Jan 20 2017 *)

NextPrime[pn# + 1] - pn# - 1

More terms from Michael De Vlieger, Jan 20 2017

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User: Olivier Bélot

A303214 Prime numbers whose average with the previous prime is not divisible by 2 or 3.

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