A237710 Least prime p < n with pi(n-p) a square, or 0 if such a prime p does not exist.

0, 0, 2, 2, 3, 5, 5, 7, 2, 2, 2, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 2, 2, 2, 2, 2, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 17, 17, 17, 19, 19, 23, 23, 23, 23, 29, 29, 29, 2, 2, 2, 2, 2, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13

Offset: 1

Author

Zhi-Wei Sun, Feb 12 2014

Keywords

• nonn

Comments

According to the conjecture in A237706, a(n) should be positive for all n > 2.

Examples

			a(5) = 3 since pi(5-3) = 1^2, but pi(5-2) = 2 is not a square.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
• Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

Crossrefs

Cf. A000040, A000290, A000720, A237706.

Programs

Mathematica

SQ[n_]:=IntegerQ[Sqrt[n]]
q[n_]:=SQ[PrimePi[n]]
Do[Do[If[q[n-Prime[k]],Print[n," ",Prime[k]];Goto[aa]],{k,1,PrimePi[n-1]}];
Print[n," ",0];Label[aa];Continue,{n,1,100}]
lp[n_]:=Module[{p=2},While[!IntegerQ[Sqrt[PrimePi[n-p]]],p=NextPrime[p]];p]; Join[{0,0},Array[ lp,80,3]] (* Harvey P. Dale, Jan 28 2024 *)