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

1,1

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

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]<l[i+1], [2$2, 4$2][s], [5, 3$2, 5][s]))
      od; is(s=4)
    end:
select(isprime and q, [$1..15000])[];  # 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 *)

Prog

(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

Crossrefs

Cf. A062351, A062352, A156116, A367735.

Sequence in context: A069791 A167846 A303918 * A228625 A356947 A214732

Adjacent sequences: A371375 A371376 A371377 * A371379 A371380 A371381

Keyword

nonn,base,fini

Author

James S. DeArmon, Mar 20 2024

Extensions

More terms from Michael S. Branicky, Mar 20 2024

Status

approved