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 A216262 Primes p such that, for p < q < r three consecutive primes, p + 2q + 2r, 2p + q + 2r and 2p + 2q + r are all primes. 1
 10193, 12113, 17683, 19501, 63743, 70793, 74317, 74797, 79657, 89231, 109073, 112657, 114371, 116993, 119237, 120431, 130211, 139801, 148573, 152123, 164881, 173867, 201623, 230017, 264919, 275543, 284927, 290761, 323537, 325643, 371873, 382777, 385193, 396061, 399403, 402817, 415201, 421273 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From first 10^5 primes, only 92 are terms. Indices of primes are 1252, 1451, 2032,..., 95460, 97950, 98973. Note that p == q == r (mod 6), e.g., {10193, 10211, 10223} == 5 mod 6 and {17683, 17707, 17713} == 1 mod 6. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE a(1) = p = 10193; s = {p, q, r} = {10193, 10211, 10223}; {{1,2,2}.s, {2,1,2}.s, {2,2,1}.s} = {51061, 51043, 51031} all primes. MATHEMATICA pr=Partition[Prime[Range[40000]], 3, 1]; Reap[Do[s=pr[[k]]; If[Union[PrimeQ[{{1, 2, 2}.s, {2, 1, 2}.s, {2, 2, 1}.s}]]=={True}, Sow[Prime[k]]], {k, Length[pr]}]][[2, 1]] tcpQ[{p_, q_, r_}]:=AllTrue[{p+2q+2r, 2p+q+2r, 2p+2q+r}, PrimeQ]; Select[ Partition[ Prime[Range[36000]], 3, 1], tcpQ][[All, 1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 03 2017 *) CROSSREFS Sequence in context: A128878 A050267 A102326 * A243410 A221119 A105582 Adjacent sequences: A216259 A216260 A216261 * A216263 A216264 A216265 KEYWORD nonn AUTHOR Zak Seidov, Mar 15 2013 STATUS approved

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Last modified June 5 07:21 EDT 2023. Contains 363130 sequences. (Running on oeis4.)