A008470 At least 3 out of 10m+1, 10m+3, 10m+7, 10m+9 are primes.

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

Author

Olivier Gérard

Keywords

• nonn

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)

Programs

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

Formula

m is a term <=> primepi(10m+10) > primepi(10m)+2. - M. F. Hasler, Mar 03 2014

Extensions

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