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A008470
At least 3 out of 10m+1, 10m+3, 10m+7, 10m+9 are primes.
5
1, 4, 7, 10, 13, 19, 22, 31, 43, 46, 61, 64, 82, 85, 88, 103, 106, 109, 130, 142, 145, 148, 160, 166, 169, 178, 187, 199, 208, 238, 268, 271, 316, 325, 346, 367, 376, 391, 400, 409, 415, 421, 451, 472, 478, 493, 523, 541, 544, 547, 550, 565, 574, 586, 670, 682
OFFSET
1,2
COMMENTS
From M. F. Hasler, Mar 03 2014: (Start)
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.
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)
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..14513 (all terms <= 10^6)
FORMULA
m is a term <=> primepi(10m+10) > primepi(10m)+2. - M. F. Hasler, Mar 03 2014
PROG
(PARI) is_A008470(m)=primepi(10*m+10) > primepi(10*m)+2. \\ M. F. Hasler, Mar 03 2014
(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
(Python)
from sympy import isprime
def ok(m): return sum(isprime(10*m+i) for i in [1, 3, 7, 9]) >= 3
print(list(filter(ok, range(700)))) # Michael S. Branicky, Sep 12 2021
CROSSREFS
Sequence in context: A173178 A348156 A287555 * A002640 A096675 A069212
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(45) and beyond from Michael S. Branicky, Sep 12 2021
STATUS
approved

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Last modified September 20 17:28 EDT 2024. Contains 376075 sequences. (Running on oeis4.)