A112529 -id:A112529 - cp's OEIS frontend

A112530 Numbers k such that prime(k) +/- k and prime(k) +/- 2k are all primes.

720, 1920, 5580, 14370, 17160, 21090, 26040, 28560, 38280, 43680, 43890, 50730, 60090, 77850, 100800, 104760, 120060, 125190, 155100, 167850, 171780, 193260, 202470, 206460, 211860, 217830, 221880, 224070, 249900, 249990, 252420, 261960

Offset: 1

Zak Seidov, Sep 10 2005

nonn

Are all terms divisible by 30?

Union of A064403 and A112529.

Harvey P. Dale, Table of n, a(n) for n = 1..228(all terms up to 5 million)

Cf. A064403, A112529.

Select[Range[720, 2000000, 10], PrimeQ[Prime[ # ]+# ]&&PrimeQ[Prime[ # ]-# ]&&PrimeQ[Prime[ # ]+2# ]&&PrimeQ[Prime[ # ]-2# ]&]
Select[Range[262000],AllTrue[Prime[#]+{#,-#,2#,-2#},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 02 2021 *)

A174189 Numbers k such that A000040(k) +/- A163300(k) are both prime.

Original entry on oeis.org

1, 7, 9, 12, 24, 30, 36, 63, 90, 102, 117, 126, 135, 150, 156, 165, 171, 180, 183, 225, 234, 270, 285, 369, 390, 399, 402, 447, 456, 501, 507, 537, 570, 582, 624, 627, 642, 651, 654, 660, 720, 735, 762, 777, 855, 864, 870, 885, 930, 936, 945

Offset: 1

Juri-Stepan Gerasimov, Mar 11 2010

nonn

			a(1) = 1 because 2-0 = 2 is prime, and 2+0 = 2 is prime.
a(2) = 7 because 17-14 = 3 is prime, and 17+14 = 31 is prime.
a(3) = 9 because 23-18 = 5 is prime, and 23+18 = 41 is prime.

Cf. A000040, A112529, A163300.

a(n) = A112529(n-1) for n >= 2. - Georg Fischer, Oct 24 2018

Corrected (11 replaced by 12, 128 replaced by 126) and extended by R. J. Mathar, Apr 16 2010

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A112530 Numbers k such that prime(k) +/- k and prime(k) +/- 2k are all primes.

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A174189 Numbers k such that A000040(k) +/- A163300(k) are both prime.

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