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

1,1

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.

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.

Example

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

Mathematica

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

Crossrefs

Cf. A000203, A007373.

Sequence in context: A231758 A215962 A084028 * A007260 A005904 A207078

Adjacent sequences: A283549 A283550 A283551 * A283553 A283554 A283555

Keyword

nonn

Author

Amiram Eldar, Mar 10 2017

Status

approved