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

1,2

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

Adjacent sequences: A008467 A008468 A008469 * A008471 A008472 A008473

Keyword

nonn

Author

Olivier Gérard

Extensions

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

Status

approved