A176682 -id:A176682 - cp's OEIS frontend

A176683 Numbers k such that k^2 +-11 are primes.

90, 120, 210, 270, 300, 510, 690, 720, 780, 960, 1200, 2190, 4260, 4350, 4470, 4920, 4980, 5040, 5100, 5250, 5550, 5670, 5730, 5790, 6810, 8100, 8280, 8490, 8610, 9150, 9540, 9990, 10140, 10200, 10650, 11130, 11430, 12060, 12510, 12930, 13770, 13800

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

nonn

			90 is in the sequence, because 90^2 - 11 = 8089 and 90^2 + 11 = 8111 are primes.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A097698, A108701, A176681, A176682

Select[Range[8! ],PrimeQ[ #^2-11]&&PrimeQ[ #^2+11]&]
Select[Range[14000],AllTrue[#^2+{11,-11},PrimeQ]&] (* Harvey P. Dale, Aug 03 2024 *)

A176684 Numbers k such that k^3 +-5 are primes.

Original entry on oeis.org

2, 12, 48, 66, 78, 126, 192, 324, 576, 738, 858, 1806, 2466, 2496, 2688, 3186, 3276, 3978, 4092, 4248, 4404, 4884, 5034, 5274, 5352, 5898, 6018, 6198, 6396, 6408, 6516, 6708, 6852, 7368, 7914, 8304, 8628, 8658, 8904, 9048, 9168, 9528, 10812, 10932

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

nonn

			12 is in the sequence, because 12^3 - 5 = 1723 and 12^3 + 5 = 1733 are primes.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A090121, A097698, A108701, A143904, A176681, A176682, A176683

Select[Range[8! ],PrimeQ[ #^3-5]&&PrimeQ[ #^3+5]&]

A176685 Numbers k such that k^3 +-7 are primes.

Original entry on oeis.org

36, 114, 174, 264, 426, 444, 810, 894, 900, 2724, 3876, 4140, 4386, 4446, 4686, 4884, 5910, 5940, 6240, 6294, 6534, 6624, 7044, 7206, 7314, 7326, 7470, 8076, 8676, 9120, 9216, 9270, 9546, 9900, 10926, 11040, 11934, 12114, 12510, 14004, 14034, 14100

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

nonn

			36 is in the sequence, because 36^3 - 7 = 46649 and 36^3 + 7 = 46663 are primes.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A090121, A097698, A108701, A143904, A176681, A176682, A176683, A176684

Select[Range[8! ],PrimeQ[ #^3-7]&&PrimeQ[ #^3+7]&]
Select[Range[15000],AllTrue[#^3+{7,-7},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 28 2020 *)

A248738 Least number m such that both m^2 -/+ prime(n) are (positive) primes.

Original entry on oeis.org

3, 4, 6, 6, 90, 4, 6, 30, 6, 180, 6, 12, 30, 18, 12, 48, 60, 90, 24, 30, 18, 120, 12, 510, 10, 60, 36, 12, 60, 12, 12, 30, 12, 12, 30, 120, 24, 48, 18, 48, 690, 1020, 30, 14, 18, 420, 180, 18, 36, 540, 42, 1230, 150, 870, 36, 18, 330, 870, 18, 30, 18, 18, 18, 150, 30, 18, 30, 30, 60, 180, 24, 30, 36

Offset: 1

Zak Seidov, Oct 13 2014

nonn

			a(1)=3 because p=prime(1)=2 and both P=3^2-2=7 and Q=3^2+2=11 are prime;
a(3)=6 because p=5 and both P=31 and Q=41 are prime;
a(10000)=510 because p=104729 and both P=155371 and Q=364829 are prime.

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A108701, A153975, A176681, A176682, A176683, A177833.

lnm[n_]:=Module[{m=2,pr=Prime[n]},If[m^2-pr<0,m=Ceiling[Sqrt[pr]]];While[ !AllTrue[m^2+{pr,-pr},PrimeQ],m++];m]; Array[lnm,80] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 22 2014 *)

a(n) = { p = prime(n); m = sqrtint(p); until( isprime(m^2-p) && isprime(m^2+p), m++); m} \\ Michel Marcus, Oct 13 2014

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A176683 Numbers k such that k^2 +-11 are primes.

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A176684 Numbers k such that k^3 +-5 are primes.

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Mathematica

A176685 Numbers k such that k^3 +-7 are primes.

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Mathematica

A248738 Least number m such that both m^2 -/+ prime(n) are (positive) primes.

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Mathematica

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