A367735 Prime numbers wherein digit values increase, decrease, and finally increase.

1201, 1213, 1217, 1301, 1303, 1307, 1319, 1327, 1409, 1423, 1427, 1429, 1439, 1523, 1549, 1601, 1607, 1609, 1613, 1619, 1627, 1637, 1657, 1709, 1723, 1747, 1759, 1801, 1823, 1847, 1867, 1879, 1901, 1907, 1913, 1949, 1979, 2309, 2417, 2423, 2437, 2503, 2539

Offset

1,1

Comments

Terms must have at least 4 digits.

There are 3287310 terms, with the last being 1245678987653210123456789. - Michael S. Branicky, Jan 26 2024

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Michael S. Branicky, Python program producing full sequence

James S. DeArmon, Python program for A367735

Example

The first term is 1201: increases 1-2, decreases 2-0, then increases 0-1.  An example 7-digit term is 1215679.

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, Jan 26 2024

Prog

(Python)
from sympy import isprime
from itertools import combinations, islice
def agen(): # generator of terms
    for d in range(4, 28):
        print(d)
        passed = set()
        for d1 in range(2, min(d-2, 9)+1):
            for c1 in combinations("123456789", d1):
                for d2 in range(1, min(d-d1-1, 10)+1):
                    digits2 = list(map(str, range(int(c1[-1])-1, -1, -1)))
                    for c2 in combinations(digits2, d2):
                        digits3 = list(map(str, range(int(c2[-1])+1, 11)))
                        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, Jan 26 2024

Crossrefs

Cf. A062351, A062352, A156116.

Sequence in context: A107520 A268877 A282015 * A217656 A020390 A156620

Adjacent sequences: A367732 A367733 A367734 * A367736 A367737 A367738

Keyword

nonn,base,fini

Author

James S. DeArmon, Jan 24 2024

Status

approved