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

1,1

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.

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!

Example

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

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 *)

Prog

(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

Crossrefs

Intersection of A030144 and A029743.

Cf. A000040, A030141.

Sequence in context: A030144 A343590 A343591 * A156756 A225659 A068690

Adjacent sequences: A323575 A323576 A323577 * A323579 A323580 A323581

Keyword

nonn,base,fini,full

Author

Bernard Schott, Jan 18 2019

Status

approved