A283552 Numbers k == 33 (mod 60) such that 2k+1, 2k+5, 3k+2 and 3k+8 are all primes.

33, 153, 453, 1953, 4773, 19353, 23253, 36273, 37413, 38793, 40773, 50133, 51693, 70413, 70833, 83433, 88893, 108393, 115233, 117873, 131193, 136113, 157773, 161733, 164793, 170973, 184533, 221793, 234813, 238293, 258453, 271893, 272313, 287313, 304953, 307713, 325533, 327753, 330393

Offset: 1

Author

Amiram Eldar, Mar 10 2017

Keywords

• nonn

Comments

Andreas Weingartner used the first 913685 terms of this sequence to prove that the equation sigma(x) = sigma(x+k) has at least one solution for every even k in the range 2 <= k <= 10^(10^7). The upper bound is just lower than the product of 2a(n)+1 of these terms which equals 3.222... * 10^10000007.

Examples

			a(2) = 153, 2*153 + 1 = 307, 2*153 + 5 = 311, 3*153 + 2 = 461 and 3*153 + 8 = 467 are all primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• A. Weingartner, On the Solutions of sigma(n) = sigma(n+k), Journal of Integer Sequences, Vol. 14 (2011), #11.5.5.

Crossrefs

Cf. A000203, A007373.

Programs

Mathematica

Select[33 + Range[0, 6*10^5]*60, PrimeQ[2 # + 1] && PrimeQ[2 # + 5] && PrimeQ[3 # + 2] && PrimeQ[3 # + 8] &]