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A323578
Primes with distinct digits for which parity of digits alternates.
3
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.
Sequence in context: A030144 A343590 A343591 * A156756 A225659 A068690
KEYWORD
nonn,base,fini,full
AUTHOR
Bernard Schott, Jan 18 2019
STATUS
approved