A146315 -id:A146315 - cp's OEIS frontend

A146318 Prime subtrahends of nearest cubes producing prime differences.

3, 5, 41, 47, 53, 59, 61, 127, 137, 149, 157, 163, 173, 179, 193, 197, 199, 211, 349, 373, 409, 433, 439, 499, 509, 727, 743, 761, 773, 809, 821, 827, 863, 887, 911, 929, 941, 947, 953, 971, 977, 983, 997, 1361, 1381, 1447, 1451, 1459, 1471, 1487, 1489, 1499

Offset: 1

Enoch Haga, Oct 30 2008

Terms in A146317 + A146318 produce a cube

			a(3)=41 because when the prime 23 is subtracted from the cube 64, the result is another prime, 41

A146315 A146316 A146317

10 'cu less pr are prime 20 N=1:O=1 30 A=3:S=sqrt(N) 40 B=N\A 50 if B*A=N then 120 60 A=A+2 70 if A<=S then 40 80 R=O^3:Q=R-N 90 if N

A146316 Prime subtrahends of nearest squares producing prime differences.

Original entry on oeis.org

2, 2, 5, 3, 2, 7, 5, 2, 11, 5, 3, 2, 17, 11, 3, 17, 13, 7, 5, 2, 23, 17, 5, 3, 2, 29, 23, 17, 5, 31, 17, 13, 11, 7, 2, 17, 11, 3, 2, 41, 23, 17, 5, 29, 19, 13, 7, 5, 29, 23, 17, 3, 2, 41, 23, 11, 2, 47, 43, 41, 37, 23, 19, 17, 13, 53, 47, 41, 11, 5, 3, 2, 59, 53, 47, 5, 3, 2, 67, 59, 47, 37

Offset: 1

Enoch Haga, Oct 30 2008

Terms in A146315 + A146316 produce a square

			a(6)=7 because when the prime 29 is subtracted from the square 36, the result is another prime, 7

A146315 A146317 A146318

10 'sq less pr are prime 20 N=1:O=1:C=1 30 A=3:S=sqrt(N) 40 B=N\A 50 if B*A=N then 120 60 A=A+2 70 if A<=S then 40 80 R=O^2:Q=R-N 90 if N31 then stop 120 N=N+2:if N

A146317 Prime differences of primes subtracted from nearest cube.

Original entry on oeis.org

5, 3, 23, 17, 11, 5, 3, 89, 79, 67, 59, 53, 43, 37, 23, 19, 17, 5, 163, 139, 103, 79, 73, 13, 3, 2, 257, 239, 227, 191, 179, 173, 137, 113, 89, 71, 59, 53, 47, 29, 23, 17, 3, 367, 347, 281, 277, 269, 257, 241, 239, 229, 197, 179, 157, 149, 131, 127, 109, 107, 101, 71, 61

Offset: 1

Enoch Haga, Oct 30 2008

Terms in A146317 + A146318 produce a cube

			a(3)=23 because when the prime 23 is subtracted from the cube 64, the result is another prime, 41

Robert Israel, Table of n, a(n) for n = 1..10000

A146315 A146316 A146318

R:= NULL: count:= 0: p:= 1:
while count < 100 do
  p:= nextprime(p);
  d:= ceil(p^(1/3))^3-p;
  if isprime(d) then count:= count+1; R:= R, d fi;
od:
R; # Robert Israel, Aug 06 2019

10 'cu less pr are prime 20 N=1:O=1 30 A=3:S=sqrt(N) 40 B=N\A 50 if B*A=N then 120 60 A=A+2 70 if A<=S then 40 80 R=O^3:Q=R-N 90 if N

A146757 Number of primes p < 10^n such that s - p is prime, where s is the next square greater than p.

Original entry on oeis.org

2, 15, 68, 363, 2084, 13567, 95164, 705036, 5444255, 43211106, 351904307, 2921904565

Offset: 1

Enoch Haga, Nov 02 2008

The number of primes p in the range 2 <= p <= 10^n for which The distance to the next larger square (A068527(p)) is also a prime. - R. J. Mathar, Sep 26 2011

			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}.

Cf. A146315, A146758, A146759, A146760.

Table[Length[Select[Prime[Range[PrimePi[10^n]]], PrimeQ[Ceiling[Sqrt[#]]^2 - #] &]], {n, 6}] (* T. D. Noe, Mar 31 2013 *)

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

Name clarified by T. D. Noe, Mar 31 2013

a(8)-a(12) from Chai Wah Wu, Jun 22 2019

cp's OEIS Frontend

A146318 Prime subtrahends of nearest cubes producing prime differences.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

UBASIC

A146316 Prime subtrahends of nearest squares producing prime differences.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

UBASIC

A146317 Prime differences of primes subtracted from nearest cube.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

UBASIC

A146757 Number of primes p < 10^n such that s - p is prime, where s is the next square greater than p.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

UBASIC

Extensions