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A283869
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Primes p such that p+12, (p+1)/2, and (p+13)/2 are also prime.
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2
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61, 661, 1201, 4261, 5101, 6121, 6361, 12421, 12541, 12841, 13921, 15361, 17041, 18301, 19801, 21661, 26821, 31321, 36901, 47521, 54121, 55921, 56101, 71341, 80701, 83221, 87421, 91381, 101161, 107761, 109441, 126481, 128461, 129841, 131101, 135601, 146941, 151141, 151561
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OFFSET
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1,1
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COMMENTS
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Numbers k such that both k and k + 12 are terms of A005383.
All terms are of the form 60*m + 1 for m > 0 since A005383(i) == 1 (mod 12) for i > 2 and if A005383(i) + 12 is a term in A005383, then A005383(i) == 1 (mod 10).
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LINKS
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FORMULA
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a(n) == 1 (mod 60).
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EXAMPLE
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61 is a term because 61 and 73 are both terms in A005383.
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MATHEMATICA
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Select[Range@ 160000, Mod[#, 60] == 1 && PrimeQ[#] && PrimeQ[# + 12] && PrimeQ[(# + 1)/2] && PrimeQ[(# + 13)/2] &] (* Indranil Ghosh, Mar 17 2017 *)
Select[Range[1, 152000, 60], AllTrue[{#, #+12, (#+1)/2, (#+13)/2}, PrimeQ]&] (* Harvey P. Dale, Oct 14 2021 *)
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PROG
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(PARI) is(n)=n%60==1 && isprime(n) && isprime(n+12) && isprime((n+1)/2) && isprime((n+13)/2) \\ Charles R Greathouse IV, Mar 17 2017
(Python)
from sympy import isprime
[i for i in range(1, 160001) if i%60 == 1 and isprime(i) and isprime(i + 12) and isprime((i + 1)/2) and isprime((i + 13)/2)] # Indranil Ghosh, Mar 17 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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