A371390 Numbers k such that prime(k), prime(k+1), prime(k+2), prime(k+3) and prime(k+4) all have the same last digit.

11582, 17385, 19317, 20579, 22931, 42098, 51895, 52252, 55259, 60393, 62192, 62193, 62680, 64050, 65324, 71483, 76391, 76773, 76805, 77052, 81139, 86711, 95661, 100208, 102032, 113646, 113892, 113954, 115251, 124227, 125218, 125586, 144165, 144299, 147619, 147620

Offset: 1

Author

Michel Lagneau, Mar 20 2024

Keywords

• nonn
• base

Examples

			11582 is a term because prime(11582) = 123229, prime(11583) = 123239, prime(11584) = 123259, prime(11585) = 123269 with the same last digit 9.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• David A. Corneth, PARI program

Crossrefs

Cf. A000040, A007652, A107730, A129750.

Programs

Maple

nn:=15*10^4:d:=array(1..5):
for n from 1 to nn do:
 for k from 1 to 5 do:
   d[k]:=irem(ithprime(n+k-1),10):
 od:
  if d[1]=d[2] and d[1]=d[3] and
d[1]=d[4] and d[1]=d[5]
    then
     printf(`%d, `,n):
    else
  fi:
od:

PARI

\\ See PARI link

Python

from itertools import count, islice
from sympy import nextprime
def A371390_gen(): # generator of terms
    xlist, p = [2, 3, 5, 7, 1], 11
    for k in count(1):
        if len(set(xlist)) == 1:
            yield k
        p = nextprime(p)
        xlist = xlist[1:]+[p%10]
A371390_list = list(islice(A371390_gen(),10)) # Chai Wah Wu, Apr 13 2024