

A146759


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


3



2, 7, 43, 224, 1355, 9306, 66200, 500249, 3883527, 31081813, 254358928
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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]]^3n]; 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, C1: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=RN
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



