A297408 Where the prime race among 10k+1, ..., 10k+9 changes leader.

2, 13, 157, 193, 347, 383, 587, 673, 907, 1163, 1327, 1483, 1907, 1933, 2897, 4723, 5557, 5573, 6037, 6113, 6637, 6673, 7487, 8273, 8317, 8363, 8387, 8443, 8467, 8573, 8647, 8803, 8837, 8933, 9277, 9293, 10067, 10103, 11897, 11923, 12037, 12073, 12107, 12143

Offset: 1

Author

Sean A. Irvine, Dec 29 2017

Keywords

• nonn

Comments

A007355 appears to be an erroneous version of this sequence.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000
• Robert G. Wilson v, Letter to N. J. A. Sloane, Aug. 1993

Crossrefs

Cf. A007352, A007350, A007353, A007354, A274121, A274122, A274123, A297406, A297407, A297408, A297410, A297411.

Programs

PARI

a297408(limit)={my(v=vector(10),vm=0,ivm=0,imv); forprime(p=2,limit,my(m=p%10);v[m]++;my(mv=vecmax(v,&imv));if(mv>vm,if(imv!=ivm,print1(p,", "); ivm=imv);vm=mv))};
a297408(12500) \\ Hugo Pfoertner, Jul 25 2021

Python

from sympy import nextprime
from itertools import islice
def agen():
    c, p, leader = [0 for i in range(10)], 1, None
    while True:
        p = nextprime(p); last = p%10; c[last] += 1; m = max(c)
        if c.count(m) == 1 and c.index(m) == last and last != leader:
            yield p; leader = last
print(list(islice(agen(), 44))) # Michael S. Branicky, Dec 20 2022