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A359332
Numbers with arithmetic derivative which is a palindromic prime number (A002385).
0
6, 10, 114, 130, 174, 182, 222, 231, 255, 273, 286, 298, 357, 358, 455, 574, 622, 870, 1015, 1309, 1335, 1677, 1695, 12594, 13630, 13686, 15258, 18534, 18654, 19082, 19114, 19522, 19626, 19922, 19986, 20998, 21558, 22178, 22882, 22930, 23062, 23262, 23709, 24338
OFFSET
1,1
COMMENTS
A subsequence of A157037.
If p and q,(p < q), are twin primes and q is a term in A002385, then m = 2*p is a term. Indeed, m' = (2*p)' = p + 2 = q, which is a palindromic prime number (A157037).
EXAMPLE
6' = 5 = A002385(3).
114' = 101 = A002385(6).
MAPLE
d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
q:= n-> (k-> isprime(k) and StringTools[IsPalindrome](""||k))(d(n)):
select(q, [$1..25000])[]; # Alois P. Heinz, Jan 29 2023
MATHEMATICA
d[0] = d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[25000], PrimeQ[p = d[#]] && PalindromeQ[p] &] (* Amiram Eldar, Jan 29 2023 *)
PROG
(Magma) f:=func<n |n le 1 select 0 else n*(&+[Factorisation(n)[i][2] / Factorisation(n)[i][1]: i in [1..#Factorisation(n)]])>; pal:=func<n|Intseq(n) eq
Reverse(Intseq(n))>; [p:p in [1..25000]|pal(Floor(f(p)) and IsPrime(Floor(f(p)))];
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Marius A. Burtea, Jan 29 2023
STATUS
approved