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A283552 Numbers k == 33 (mod 60) such that 2k+1, 2k+5, 3k+2 and 3k+8 are all primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A231758 A215962 A084028 * A007260 A005904 A207078
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 10 2017
STATUS
approved

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Last modified July 24 22:37 EDT 2024. Contains 374585 sequences. (Running on oeis4.)