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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 04:52 EST 2021. Contains 349562 sequences. (Running on oeis4.)