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A350400
a(n) is the least k with A350399(k) = n, or 0 if there is no such k.
2
1, 3, 7, 11, 21, 24, 30, 60, 42, 45, 63, 75, 90, 135, 147, 198, 165, 105, 252, 264, 180, 399, 513, 375, 270, 210, 330, 405, 654, 255, 315, 345, 465, 480, 570, 555, 390, 1020, 675, 798, 777, 1110, 900, 660, 585, 525, 855, 825, 960, 630, 924, 735, 1419, 1305, 840, 975, 780, 1350, 945, 1050, 1500
OFFSET
0,2
COMMENTS
Conjecture: a(n) > 0 for all n.
LINKS
EXAMPLE
a(3) = 11 because A350399(11) = 3 and this is the first appearance of 3 in A350399.
MAPLE
f:= proc(k) local P, i;
P:= select(t -> isprime(t) and isprime(2*k-t) and isprime(-t^2 mod (2*k)), [2, seq(i, i=3..k, 2)]);
nops(P);
end proc:
N:= 60: # for a(0) to a(N)
V:= Array(0..N): count := 0:
for k from 1 while count < N+1 do
v:= f(k);
if v <= N and V[v] = 0 then
count:= count+1;
V[v]:= k;
fi;
od:
convert(V, list);
MATHEMATICA
a[n_] := Count[Select[Range[2, 2*n], PrimeQ], _?(# >= n && PrimeQ[2*n - #] && PrimeQ[Mod[#*(2*n - #), 2*n]] &)]; seq[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[n < nmax && c < len, i = a[n] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; TakeWhile[s, # > 0 &]]; seq[60, 10^4] (* Amiram Eldar, Dec 30 2021 *)
CROSSREFS
Cf. A350399.
Sequence in context: A061258 A057660 A130972 * A344483 A151923 A187264
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Dec 28 2021
STATUS
approved