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
Examples
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}.
Programs
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Mathematica
Table[Length[Select[Prime[Range[PrimePi[10^n]]], PrimeQ[Ceiling[Sqrt[#]]^2 - #] &]], {n, 6}] (* T. D. Noe, Mar 31 2013 *) -
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
1 print R;N;Q;C:N=N+2:C=C+1:goto 30 100 N=N+2:if N
Extensions
Name clarified by T. D. Noe, Mar 31 2013
a(8)-a(12) from Chai Wah Wu, Jun 22 2019
Comments