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, 2120975833

Offset: 1

Author

Enoch Haga, Nov 02 2008

Keywords

• nonn
• more

Examples

			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}.
		

Crossrefs

Cf. A006880, A146756, A146757, A146760.

Programs

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 *)

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

PARI

list(nmax) = {my(m = 0, c = 2, cc = c^3, n = 0, pow = 10); forprime(p = 1, , if(p > pow, print1(m, ", "); n++; if(n == nmax, break); pow *= 10); if(p > cc, c++; cc = c^3); if(isprime(cc - p), m++));} \\ Amiram Eldar, Jan 20 2025

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 N1 print R;N;Q;C:N=N+2:C=C+1:goto 30
100 N=N+2:if N
				

Extensions

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

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

a(12) from Amiram Eldar, Jan 20 2025