A357373 a(n) is the first prime p such that (p+q)/(2*n) is the square of a prime, where q is the next prime after p.

3, 17, 11, 47521, 43, 149, 26041, 71, 79, 3607, 97, 107, 6871, 53, 59, 61, 31397, 71, 73, 179, 2539, 197, 2777, 599, 223, 647, 107, 61843, 1520777, 113, 277, 283, 823, 5743, 313, 139, 254887, 337, 349, 157, 75797, 1049, 5197, 173, 179, 409, 2297, 191, 439, 6047, 457, 892357, 8951, 242399, 491

Offset

1,1

Links

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

Example

a(3) = 11 because (11+13)/(2*3) = 4 = 2^2 where 2 is prime, and 11 is the first prime that works.

Maple

f:= proc(n) local r, v, p, q;
   r:= 1:
   do
     r:= nextprime(r);
     v:= n*r^2;
     p:= prevprime(v);
     if 2*v-p = nextprime(v) then return p fi
   od
end proc:
map(f, [$1..100]);

Mathematica

f[n_] := Module[{r, v, p, q}, r = 1; While[True, r = NextPrime[r]; v = n*r^2; p = NextPrime[v, -1]; If[2*v - p == NextPrime[v], Return[p]]]];
Table[f[n], {n, 1, 100}] (* Jean-François Alcover, Oct 16 2022, after Robert Israel *)

Crossrefs

Cf. A357369

Sequence in context: A033467 A096475 A088122 * A273702 A273710 A087964

Adjacent sequences: A357370 A357371 A357372 * A357374 A357375 A357376

Keyword

nonn

Author

Robert Israel, Sep 25 2022

Status

approved