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

KEYWORD

nonn

AUTHOR

EXTENSIONS

a(45) and beyond from Michael S. Branicky, Sep 12 2021

STATUS

approved