A146757 Number of primes p < 10^n such that s - p is prime, where s is the next square greater than p.

2, 15, 68, 363, 2084, 13567, 95164, 705036, 5444255, 43211106, 351904307, 2921904565

Offset

1,1

Comments

The number of primes p in the range 2 <= p <= 10^n for which The distance to the next larger square (A068527(p)) is also a prime. - R. J. Mathar, Sep 26 2011

Links

Table of n, a(n) for n=1..12.

Example

A(2) = 15 because at 10^2 there are 15 primes that, subtracted from the next higher value square, produce prime differences: {2, 7, 11, 13, 23, 29, 31, 47, 53, 59, 61, 79, 83, 89, 97}.

Mathematica

Table[Length[Select[Prime[Range[PrimePi[10^n]]], PrimeQ[Ceiling[Sqrt[#]]^2 - #] &]], {n, 6}] (* T. D. Noe, Mar 31 2013 *)

Prog

(UBASIC) 10 'sq less pr are prime 20 N=1:O=1:C=1 30 A=3:S=sqrt(N):if N>10^3 then print N, C-1:stop 40 B=N\A 50 if B*A=N then 100 60 A=A+2 70 if A<=S then 40 80 R=O^2:Q=R-N 90 if N<R and N=prmdiv(N) and Q=prmdiv(Q) then if Q>1 print R; N; Q; C:N=N+2:C=C+1:goto 30 100 N=N+2:if N<R then 30:else O=O+1:goto 80

Crossrefs

Cf. A146315, A146758, A146759, A146760.

Sequence in context: A117393 A055206 A216614 * A091135 A056037 A125903

Adjacent sequences: A146754 A146755 A146756 * A146758 A146759 A146760

Keyword

more,nonn

Author

Enoch Haga, Nov 02 2008

Extensions

Name clarified by T. D. Noe, Mar 31 2013

a(8)-a(12) from Chai Wah Wu, Jun 22 2019

Status

approved