cp's OEIS Frontend

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

%I A367735 #49 Feb 05 2024 18:29:39
%S A367735 1201,1213,1217,1301,1303,1307,1319,1327,1409,1423,1427,1429,1439,
%T A367735 1523,1549,1601,1607,1609,1613,1619,1627,1637,1657,1709,1723,1747,
%U A367735 1759,1801,1823,1847,1867,1879,1901,1907,1913,1949,1979,2309,2417,2423,2437,2503,2539
%N A367735 Prime numbers wherein digit values increase, decrease, and finally increase.
%C A367735 Terms must have at least 4 digits.
%C A367735 There are 3287310 terms, with the last being 1245678987653210123456789. - _Michael S. Branicky_, Jan 26 2024
%H A367735 Alois P. Heinz, <a href="/A367735/b367735.txt">Table of n, a(n) for n = 1..10000</a>
%H A367735 Michael S. Branicky, <a href="/A367735/a367735.txt">Python program producing full sequence</a>
%H A367735 James S. DeArmon, <a href="/A367735/a367735_1.txt">Python program for A367735</a>
%e A367735 The first term is 1201: increases 1-2, decreases 2-0, then increases 0-1.  An example 7-digit term is 1215679.
%p A367735 q:= proc(n) local i, l, s;
%p A367735       l, s:= convert(n, base, 10), 1;
%p A367735       for i to nops(l)-1 while s<5 do s:=
%p A367735        `if`(l[i]=l[i+1], 5,
%p A367735        `if`(l[i]>l[i+1], [2$2, 4$2][s], [5, 3$2, 5][s]))
%p A367735       od; is(s=4)
%p A367735     end:
%p A367735 select(isprime and q, [$1..15000])[];  # _Alois P. Heinz_, Jan 26 2024
%o A367735 (Python)
%o A367735 from sympy import isprime
%o A367735 from itertools import combinations, islice
%o A367735 def agen(): # generator of terms
%o A367735     for d in range(4, 28):
%o A367735         print(d)
%o A367735         passed = set()
%o A367735         for d1 in range(2, min(d-2, 9)+1):
%o A367735             for c1 in combinations("123456789", d1):
%o A367735                 for d2 in range(1, min(d-d1-1, 10)+1):
%o A367735                     digits2 = list(map(str, range(int(c1[-1])-1, -1, -1)))
%o A367735                     for c2 in combinations(digits2, d2):
%o A367735                         digits3 = list(map(str, range(int(c2[-1])+1, 11)))
%o A367735                         for c3 in combinations(digits3, d - d1 - d2):
%o A367735                             t = int("".join(c1 + c2 + c3))
%o A367735                             if isprime(t):
%o A367735                                 passed.add(t)
%o A367735         yield from sorted(passed)
%o A367735 print(list(islice(agen(), 63))) # _Michael S. Branicky_, Jan 26 2024
%Y A367735 Cf. A062351, A062352, A156116.
%K A367735 nonn,base,fini
%O A367735 1,1
%A A367735 _James S. DeArmon_, Jan 24 2024