A381158 Prime numbers where digit values decrease while alternating parity.

2, 3, 5, 7, 41, 43, 61, 83, 521, 541, 743, 761, 941, 983, 6521, 8521, 8543, 8741, 8761, 76541, 76543, 94321, 98321, 98543

Offset: 1

Author

James S. DeArmon, Feb 15 2025

Keywords

• nonn
• base
• fini
• full

Examples

			41 is a term, since the digits decrease in value and alternate even and odd.
		

Crossrefs

Cf. A052014, A000040, A028867, A028864, A052015, A382027.

Programs

Maple

b:= proc(n) `if`(isprime(n), n, [][]), seq(b(10*n+j), j=irem(n, 10)-1..1, -2) end:
{seq(b(n), n=1..9)}[];  # Alois P. Heinz, Mar 12 2025

Mathematica

ad=Select[Prime[Range[10^6]],Reverse[Union[IntegerDigits[#]]]==IntegerDigits[#]&];fQ[n_] := Block[{m = Mod[ IntegerDigits@ n, 2]}, m == Split[m, UnsameQ][[1]]];Select[ad,fQ] (* James C. McMahon, Mar 20 2025 *)

Python

from sympy import isprime
from itertools import combinations
def ap(s): return all((s[i] in "13579") == (s[i+1] in "02468") for i in range(len(s)-1))
def afull(): return sorted(t for d in range(1, 10) for c in combinations("987654321", d) if ap(c) and isprime(t:=int("".join(c))))
print(afull()) # Michael S. Branicky, Mar 10 2025