A346028 Primes that are the first in a run of exactly 8 emirps.

334759, 9094009, 9685771, 11875307, 12503017, 19776443, 32906869, 35414443, 37376201, 70252333, 71161309, 73694129, 77454067, 93907523, 98606489, 100545637, 104827991, 112604857, 147009703, 155376791, 183766217, 187717499, 194024953, 196702423, 314716411

Offset

1,1

Comments

There are large gaps in this sequence because all terms need to begin with 1, 3, 7, or 9 otherwise the reversal is composite.

Links

Table of n, a(n) for n=1..25.

Example

a(1) = 334759 because of the 10 consecutive primes 334753, 334759, 334771, 334777, 334783, 334787, 334793, 334843, 334861, 334877 all except 334753 and 334877 are emirps and this is the first such occurrence.

Mathematica

EmQ[n_]:=(s=IntegerReverse@n; PrimeQ@s&&n!=s);
Monitor[Do[p=Prime@k; If[MemberQ[{1, 3, 7, 9}, First@IntegerDigits@p], If[Boole[EmQ/@NextPrime[p, Range[-1, 8]]]=={0, 1, 1, 1, 1, 1, 1, 1, 1, 0}, Print@p]], {k, 10^6}], p] (* Giorgos Kalogeropoulos, Jul 27 2021 *)

Prog

(Python) # uses code in A346026
print(aupto(10**7, runlength=8)) # Michael S. Branicky, Jul 14 2021

Crossrefs

Subsequence of A006567 (emirps).

Cf. A003684, A048052, A048054, A071612, A346022, A346023, A346024, A346025, A346026, A346027.

Sequence in context: A261861 A234129 A232412 * A268280 A234081 A022225

Adjacent sequences: A346025 A346026 A346027 * A346029 A346030 A346031

Keyword

nonn,base

Author

Lars Blomberg, Jul 14 2021

Status

approved