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A323578 Primes with distinct digits for which parity of digits alternates.

%I A323578 #30 Mar 14 2019 07:15:38
%S A323578 2,3,5,7,23,29,41,43,47,61,67,83,89,103,107,109,127,149,163,167,307,
%T A323578 347,349,367,389,503,509,521,523,541,547,563,569,587,701,709,743,761,
%U A323578 769,907,941,947,967,983,2143,2309
%N A323578 Primes with distinct digits for which parity of digits alternates.
%C A323578 There are 4426 terms (found by _David A. Corneth_) in this sequence, which is a subsequence of A030144.
%C A323578 The largest prime of this sequence is 987654103 which is also the largest prime with distinct digits in A029743.
%H A323578 David A. Corneth, <a href="/A323578/b323578.txt">Table of n, a(n) for n = 1..4426</a> (Complete sequence)
%H A323578 Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php/987654103.html">987654103</a>, Prime Curios!
%e A323578 2143 is a term as 2, 1, 4 and 3 have even and odd parity alternately and these four digits are all distinct.
%t A323578 {2}~Join~Select[Prime@ Range@ 350, And[Max@ Tally[#][[All, -1]] == 1, AllTrue[#[[Range[2, Length[#], 2] ]], EvenQ], AllTrue[#[[Range[1, Length[#], 2] ]], OddQ]] &@ Reverse@ IntegerDigits@ # &] (* _Michael De Vlieger_, Jan 19 2019 *)
%o A323578 (PARI) allTerms() = {my(res = List([2])); c = vector(10); odd = [1, 3, 5, 7, 9]; even = [0, 2, 4, 6, 8]; for(i = 0, 119, pi = numtoperm(5, i); vi = vector(5, k, odd[pi[k]]); for(j = 0, 119, pj = numtoperm(5, j); vj = vector(5, k, even[pj[k]]); for(m = 1, 5, c[2*m] = vi[m]; c[2*m - 1] = vj[m]; ); cv = fromdigits(c); for(m = 1, 10, if(isprime(cv % 10^m), listput(res, cv % 10^m); ) ) ) ); listsort(res, 1); res } \\ _David A. Corneth_, Jan 18 2019
%Y A323578 Intersection of A030144 and A029743.
%Y A323578 Cf. A000040, A030141.
%K A323578 nonn,base,fini,full
%O A323578 1,1
%A A323578 _Bernard Schott_, Jan 18 2019