A354589 Primes p starting a sequence of 4 consecutive primes whose final digits are 1,3,7,9 (in any order).
11, 23, 47, 53, 67, 83, 89, 101, 109, 149, 167, 191, 193, 197, 199, 211, 251, 257, 263, 383, 443, 449, 461, 487, 557, 563, 587, 593, 599, 613, 647, 659, 739, 757, 761, 821, 859, 983, 991, 1061, 1063, 1069, 1117, 1217, 1223, 1283, 1301, 1303, 1367, 1433, 1439, 1447, 1481, 1553, 1567, 1571, 1579
Offset: 1
Examples
a(3) = 47 is in the sequence because the 4 consecutive primes starting with 47 are 47, 53, 59, 61, and their final digits 7,3,9,1 are a permutation of 1,3,7,9.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
P:= select(isprime, [seq(i,i=3..2000,2)]): P1:= P mod 10: P[select(i -> convert(P1[i..i+3],set) = {1,3,7,9}, [$1..nops(P)-3])]; -
Mathematica
Select[Partition[Prime[Range[300]], 4, 1], Sort[Mod[#, 10]] == {1, 3, 7, 9} &][[;; , 1]] (* Amiram Eldar, Aug 19 2022 *) -
Python
from sympy import nextprime from itertools import islice def agen(): # generator of terms p = [2, 3, 5, 7] while True: if set(map(lambda x: x%10, p)) == {1, 3, 7, 9}: yield p[0] p = p[1:] + [nextprime(p[-1])] print(list(islice(agen(), 60))) # Michael S. Branicky, Aug 18 2022