A336409
Distance from prime(n) to the nearest odd composite that is < prime(n).
Original entry on oeis.org
2, 4, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 2, 4, 2, 4, 2, 4, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 2, 4
Offset: 5
Beginning with prime(5) = 11: 11-9 = 2, 13-9 = 4, 17-15 = 2, 19-15 = 4.
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A336409 := proc(n)
local p;
p := ithprime(n) ;
for a from p-2 by -2 do
if not isprime(a) then
return p-a ;
end if;
end do:
end proc:
seq(A336409(n),n=5..100) ; # R. J. Mathar, Oct 02 2020
# second Maple program:
a:= n-> `if`(isprime(ithprime(n)-2), 4, 2):
seq(a(n), n=5..100); # Alois P. Heinz, Oct 02 2020
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z = 5000; d = Select[Range[2, z], ! PrimeQ@# && OddQ@# &]; (* A014076 *)
f[n_] := Select[d, # < Prime[n] &];
t = Table[Prime[n] - Max[f[n]], {n, 5, 300}] (* A336409 *)
Flatten[Position[t, 2]] (* A336410 *)
Flatten[Position[t, 4]] (* A336411 *)
A383134
Array read by ascending antidiagonals: A(n,k) is the length of the arithmetic progression of only primes having difference n and first term prime(k).
Original entry on oeis.org
2, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 2, 3, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1
The array begins as:
2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 3, 2, 1, 2, 1, 2, 1, 1, 2, ...
2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 3, 1, 2, 1, 2, 1, 2, 1, 1, ...
2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 5, 3, 4, 2, 3, 1, 2, 1, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 3, 2, 1, 2, 1, 1, 1, 2, 2, ...
2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 3, 1, 2, 1, 2, 1, 2, 1, 1, ...
...
A(2,2) = 3 since 3 primes are in arithmetic progression with a difference of 2 and the first term equal to the 2nd prime: 3, 5, and 7.
A(6,3) = 5 since 5 primes are in arithmetic progression with a difference of 6 and the first term equal to the 3rd prime: 5, 11, 17, 23, and 29.
- Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 139.
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A[n_,k_]:=Module[{count=1,sum=Prime[k]},While[PrimeQ[sum+=n], count++]; count]; Table[A[n-k+1,k],{n,13},{k,n}]//Flatten
Showing 1-2 of 2 results.