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