A146318 -id:A146318 - cp's OEIS frontend

A146315 Prime differences of primes subtracted from nearest square.

2, 7, 11, 13, 23, 29, 31, 47, 53, 59, 61, 79, 83, 89, 97, 127, 131, 137, 139, 167, 173, 179, 191, 193, 223, 227, 233, 239, 251, 293, 307, 311, 313, 317, 359, 383, 389, 397, 439, 443, 461, 467, 479, 547, 557, 563, 569, 571, 647, 653, 659, 673, 727, 743, 761, 773

Offset: 1

Enoch Haga, Oct 30 2008

Terms in A146315 + A146316 produce a square

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

Cf. A146316 - 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

{p in A000040: A068527(p) in A000040}. - R. J. Mathar, Sep 26 2011

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

A163850 Primes p such that their distance to the nearest cube above p and also their distance to the nearest cube below p are prime.

Original entry on oeis.org

3, 127, 24391, 29789, 328511, 2460373, 3048623, 9393929, 10503461

Offset: 1

Vladimir Joseph Stephan Orlovsky, Aug 05 2009

nonn

The two sequences A048763(p) and A048762(p), p=A000040(n), define
nearest cubes above and below each prime p. If p is in A146318, the
distance to the larger cube, A048763(p)-p, is prime. If p is
in the set {3, 11, 13, 19, 29, 67,...,107, 127, 223,..}, the distance to the lower
cube is prime. If both of these distances are prime, we insert p into the sequence.

			p=3 is in the sequence because the distance p-1=2 to the cube 1^3 below 3, and also the distance 8-p=5 to the cube 8=2^3 above p are prime.
p=127 is in the sequence because the distance p-125=2 to the cube 125=5^3 below p, and also the distance 216-p=89 to the cube 216=6^3 above p, are prime.

Cf. A163848

Clear[f,lst,p,n]; f[n_]:=IntegerPart[n^(1/3)]; lst={};Do[p=Prime[n];If[PrimeQ[p-f[p]^3]&&PrimeQ[(f[p]+1)^3-p],AppendTo[lst,p]],{n,9!}];lst
dncQ[n_]:=Module[{c=Floor[Surd[n,3]]},AllTrue[{n-c^3,(c+1)^3-n},PrimeQ]]; Select[Prime[Range[230000]],dncQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 16 2016 *)

Edited, first 5 entries checked by R. J. Mathar, Aug 12 2009

Two more terms (a(8) and a(9)) from Harvey P. Dale, Oct 16 2016

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A146315 Prime differences of primes subtracted from nearest square.

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A146316 Prime subtrahends of nearest squares producing prime differences.

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UBASIC

A146317 Prime differences of primes subtracted from nearest cube.

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A163850 Primes p such that their distance to the nearest cube above p and also their distance to the nearest cube below p are prime.

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