A359332 Numbers with arithmetic derivative which is a palindromic prime number (A002385).

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

Author

Marius A. Burtea, Jan 29 2023

Keywords

• nonn
• base

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).

Examples

			6' = 5 = A002385(3).
114' = 101 = A002385(6).
		

Crossrefs

Cf. A001097, A002113, A002385, A003415, A157037.

Programs

Magma

f:=func;
pal:=func;
[p:p in [1..25000]|pal(Floor(f(p))) and IsPrime(Floor(f(p)))];

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 *)