A146759 Number of primes p < 10^n such that c - p is prime, where c is the next cube greater than p.

2, 7, 43, 224, 1355, 9306, 66200, 500249, 3883527, 31081813, 254358928

Offset

1,1

Links

Table of n, a(n) for n=1..11.

Example

a(2) = 7 because at 10^2 there are 7 primes that, subtracted from the next higher value cube, produce prime differences: {3, 5, 41, 47, 53, 59, 61}.

Mathematica

Table[Length[Select[Prime[Range[PrimePi[10^n]]], PrimeQ[Ceiling[#^(1/3)]^3 - #] &]], {n, 6}] (* T. D. Noe, Mar 31 2013 *)
cpQ[n_]:=PrimeQ[Ceiling[Surd[n, 3]]^3-n]; nn=9; Module[{c=Table[If[ cpQ[n], 1, 0], {n, Prime[ Range[ PrimePi[ 10^nn]]]}]}, Table[ Total[ Take[c, PrimePi[10^p]]], {p, nn}]] (* Harvey P. Dale, Aug 13 2014 *)

Prog

(UBASIC)
10 'cu 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^3: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
(PARI) a(n) = {my(nb = 0); forprime(p=2, 10^n, if (isprime((sqrtnint(p, 3)+1)^3 - p), nb++); ); nb; } \\ Michel Marcus, Jun 22 2019

Crossrefs

Cf. A006880, A146756, A146757, A146760.

Sequence in context: A091877 A050631 A235714 * A303031 A220220 A144059

Adjacent sequences: A146756 A146757 A146758 * A146760 A146761 A146762

Keyword

nonn,more

Author

Enoch Haga, Nov 02 2008

Extensions

Better name and more terms from Sean A. Irvine, Mar 27 2013

a(10)-a(11) from Chai Wah Wu, Jun 21 2019

Status

approved