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At least 3 out of 10m+1, 10m+3, 10m+7, 10m+9 are primes.

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`%I #26 Sep 12 2021 16:25:08
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`%S 1,4,7,10,13,19,22,31,43,46,61,64,82,85,88,103,106,109,130,142,145,
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`%T 148,160,166,169,178,187,199,208,238,268,271,316,325,346,367,376,391,
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`%U 400,409,415,421,451,472,478,493,523,541,544,547,550,565,574,586,670,682
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`%N At least 3 out of 10m+1, 10m+3, 10m+7, 10m+9 are primes.
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`%C From _M. F. Hasler_, Mar 03 2014: (Start)
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`%C The decade m must be of the form 3k+1, since for m=3k, 10m+3 and 10m+9 cannot be prime and for m=3k+2, 10k+1 and 10k+7 cannot be prime. See A238713 for the least member of the triple, i.e., the first prime of the corresponding decade.
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`%C The first occurrence of 5 consecutive triples is: 11, 13, 17 (or 19) ; 41, 43, 47 ; 71, 73, 79 ; 101, 103, 107 (or 109) ; 131, 137, 139. This corresponds to decades 1,4,7,10,13; i.e., the first 5 terms of this sequence. The next occurrence of 4 consecutive triples starts with decade m=541, and the next occurrence of 5 consecutive triples starts with decade m=910052463685 (found by J. K. Andersen). (End)
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`%H Michael S. Branicky, <a href="/A008470/b008470.txt">Table of n, a(n) for n = 1..14513</a> (all terms <= 10^6)
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`%F m is a term <=> primepi(10m+10) > primepi(10m)+2. - _M. F. Hasler_, Mar 03 2014
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`%o (PARI) is_A008470(m)=primepi(10*m+10) > primepi(10*m)+2. \\ _M. F. Hasler_, Mar 03 2014
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`%o (PARI) is(n)=if(isprime(10*n+1), if(isprime(10*n+3), isprime(10*n+7) || isprime(10*n+9), isprime(10*n+7) && isprime(10*n+9)), isprime(10*n+3)&&isprime(10*n+7)&&isprime(10*n+9)) \\ _Charles R Greathouse IV_, Mar 03 2014
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`%o (Python)
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`%o from sympy import isprime
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`%o def ok(m): return sum(isprime(10*m+i) for i in [1, 3, 7, 9]) >= 3
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`%o print(list(filter(ok, range(700)))) # _Michael S. Branicky_, Sep 12 2021
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`%K nonn
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`%O 1,2
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`%A _Olivier GĂ©rard_
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`%E a(45) and beyond from _Michael S. Branicky_, Sep 12 2021
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