A085637 Numbers k such that k*prime(k) -+ 1 are twin primes.

2, 30, 72, 144, 312, 336, 510, 690, 990, 1122, 1254, 1272, 1410, 2082, 2376, 2508, 2586, 2664, 2802, 3060, 3096, 3180, 3432, 3510, 3684, 4062, 4506, 5526, 5790, 6174, 7224, 8064, 8388, 9078, 9390, 9504, 10698, 10794, 10884, 10992, 11046, 11334

Offset: 1

Author

Zak Seidov, Jul 11 2003

Keywords

• easy
• nonn

Comments

Intersection of A086172 and A086173. See also A086174, A086175, A086176, A086177.

Examples

			k=30 is a term because 30*prime(30) +- 1 = 3390 +- 1 are twin primes.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A086172, A086173, A086174, A086175, A086176, A086177.

Programs

Magma

[n: n in [1..11500] | IsPrime(n*NthPrime(n) - 1) and IsPrime(n*NthPrime(n) + 1) ]; // Vincenzo Librandi, Oct 05 2012

Mathematica

Select[Range[15000], PrimeQ[ # Prime[ # ] - 1] && PrimeQ[ # Prime[ # ] + 1] &]
Select[Range[12000],AllTrue[#*Prime[#]+{1,-1},PrimeQ]&] (* Harvey P. Dale, Mar 21 2025 *)