A346029 Primes that are the first in a run of exactly 9 emirps.

7904639, 120890249, 154984343, 174625597, 312700789, 318629783, 707262887, 756791029, 923780981, 958610069, 1049344897, 1068171977, 1117675201, 1194919381, 1327765591, 1368391847, 1385828243, 1846629391, 1976590081, 3117896521, 3182618969, 3322051367

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..22.

Example

a(1) = 7904639 because of the 11 consecutive primes 7904629, 7904639, 7904651, 7904653, 7904657, 7904669, 7904683, 7904707, 7904719, 7904723, 7904731 all except 7904629 and 7904731 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, 9]]]==Join[{0}, 1~Table~9, {0}], Print@p]], {k, 10^8}], p] (* Giorgos Kalogeropoulos, Jul 27 2021 *)

Prog

(Python) # uses code in A346026
print(aupto(10**7, runlength=9)) # Michael S. Branicky, Jul 14 2021

Crossrefs

Subsequence of A006567 (emirps).

Cf. A003684, A048052, A048054, A071612, A346022, A346023, A346024, A346025, A346026, A346027, A346028.

Sequence in context: A235222 A239588 A210275 * A237338 A360905 A233797

Adjacent sequences: A346026 A346027 A346028 * A346030 A346031 A346032

Keyword

nonn,base

Author

Lars Blomberg, Jul 14 2021

Status

approved