A371378 Prime numbers wherein digit values decrease, increase, and finally decrease.

1021, 1031, 1051, 1061, 1063, 1087, 1091, 1093, 1097, 2053, 2063, 2081, 2083, 2087, 2131, 2141, 2143, 2153, 2161, 3041, 3061, 3083, 3121, 3163, 3181, 3187, 3191, 3251, 3253, 3271, 4021, 4051, 4073, 4091, 4093, 4153, 4231, 4241, 4243, 4253, 4261, 4271, 4273, 4283

Offset: 1

Author

James S. DeArmon, Mar 20 2024

Keywords

• nonn
• base
• fini

Comments

Terms must have at least 4 digits. The sequence is finite.

There are 3136837 terms, with the last being 98765432101234567987654321. - Michael S. Branicky, Mar 20 2024

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Michael S. Branicky, Alternative Python program for full sequence A371378
• James S. DeArmon, LISP Code for A371378

Crossrefs

Cf. A062351, A062352, A156116, A367735.

Programs

Maple

q:= proc(n) local i, l, s;
      l, s:= convert(n, base, 10), 1;
      for i to nops(l)-1 while s<5 do s:=
       `if`(l[i]=l[i+1], 5,
       `if`(l[i]Alois P. Heinz, Mar 21 2024

Mathematica

Select[Prime[Range[600]], SplitBy[Sign[Differences[IntegerDigits[#]]], Sign][[;; , 1]] == {-1, 1, -1} &] (* Amiram Eldar, Mar 21 2024 *)

Python

from sympy import isprime
from itertools import combinations, islice
def agen(): # generator of terms
    for d in range(4, 29):
        print(d)
        passed = set()
        for d1 in range(2, min(d-2, 11)+1):
            for c1 in combinations("9876543210", d1):
                for d2 in range(1, min(d-d1-1, 10)+1):
                    digits2 = list(map(str, range(int(c1[-1])+1, 10)))
                    for c2 in combinations(digits2, d2):
                        digits3 = list(map(str, range(int(c2[-1])-1, -1, -1)))
                        for c3 in combinations(digits3, d - d1 - d2):
                            t = int("".join(c1 + c2 + c3))
                            if isprime(t):
                                passed.add(t)
        yield from sorted(passed)
print(list(islice(agen(), 63))) # Michael S. Branicky, Mar 20 2024

Extensions

More terms from Michael S. Branicky, Mar 20 2024