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

2, 3, 5, 7, 23, 29, 41, 43, 47, 61, 67, 83, 89, 103, 107, 109, 127, 149, 163, 167, 307, 347, 349, 367, 389, 503, 509, 521, 523, 541, 547, 563, 569, 587, 701, 709, 743, 761, 769, 907, 941, 947, 967, 983, 2143, 2309

Offset: 1

Author

Bernard Schott, Jan 18 2019

Keywords

• nonn
• base
• fini
• full

Comments

There are 4426 terms (found by David A. Corneth) in this sequence, which is a subsequence of A030144.

The largest prime of this sequence is 987654103 which is also the largest prime with distinct digits in A029743.

Examples

			2143 is a term as 2, 1, 4 and 3 have even and odd parity alternately and these four digits are all distinct.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..4426 (Complete sequence)
• Chris K. Caldwell and G. L. Honaker, Jr., 987654103, Prime Curios!

Crossrefs

Intersection of A030144 and A029743.

Cf. A000040, A030141.

Programs

Mathematica

{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 *)

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