A353703 Palindromes (A002113) in A157037.

6, 22, 66, 202, 222, 282, 434, 454, 474, 494, 555, 595, 838, 858, 969, 1001, 1551, 1771, 3333, 3553, 5335, 6006, 6226, 6886, 8778, 9889, 12921, 14541, 15051, 16261, 16761, 17171, 18681, 19491, 20202, 20602, 20802, 20902, 24142, 24242, 24542, 28282, 28482, 30003

Offset

1,1

Comments

Intersection of A002113 and A157037.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

22 = A002113(12) and 22 = A157037(3), so 22 is a term.
66 = A002113(16) and 22 = A157037(8), so 66 is a term.

Maple

filter:= proc(n) local t;
  isprime(n*add(t[2]/t[1], t=ifactors(n)[2]))
end proc:
digrev:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
N:= 100: # for a(1) to a(N)
Res:= 6: count:= 1:
for d from 2 while count < N do
  if d::even then
    m:= d/2;
    for n from 10^(m-1) to 10^m-1 while count < N do
      v:=  n*10^m + digrev(n);
      if filter(v) then Res:= Res, v; count:= count+1  fi;
    od
  else
    m:= (d-1)/2;
    for n from 10^(m-1) to 10^m-1 while count < N do
      for y from 0 to 9 while count < N do
        v:= n*10^(m+1)+y*10^m+digrev(n);
        if filter(v) then Res:= Res, v; count:= count+1 fi;
    od od:
  fi
od:
Res; # Robert Israel, May 09 2023

Mathematica

d[0] = d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[30003], PalindromeQ[#] && PrimeQ[d[#]] &] (* Amiram Eldar, May 09 2022 *)

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))>; [n:n in [2..30003]| pal(n) and IsPrime(Floor(f(n)))];
(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
isok(m) = my(d); isprime(ad(m)) && (d=digits(m)) && (d==Vecrev(d)); \\ Michel Marcus, May 09 2022
(Python)
from itertools import chain, count, islice
from sympy import isprime, factorint
def A353703_gen(): # generator of terms
    return filter(lambda n:isprime(sum(n*e//p for p, e in factorint(n).items())), chain.from_iterable(chain((int((s:=str(d))+s[-2::-1]) for d in range(10**l, 10**(l+1))), (int((s:=str(d))+s[::-1]) for d in range(10**l, 10**(l+1)))) for l in count(0)))
A353703_list = list(islice(A353703_gen(), 20)) # Chai Wah Wu, Jun 23 2022

Crossrefs

Cf. A002113, A003415, A157037.

Sequence in context: A189418 A027992 A271389 * A247168 A353704 A305032

Adjacent sequences: A353700 A353701 A353702 * A353704 A353705 A353706

Keyword

nonn,base

Author

Marius A. Burtea, May 08 2022

Status

approved