A359115 a(n) is the smallest odd prime not already in the sequence such that when the terms a(1)..a(n) are concatenated, the result is the reverse of a prime.

3, 5, 11, 7, 29, 37, 89, 211, 71, 241, 347, 331, 23, 457, 233, 31, 53, 67, 17, 181, 107, 1051, 173, 421, 113, 103, 491, 601, 1607, 223, 1187, 1093, 257, 643, 839, 1021, 557, 2731, 1301, 1213, 761, 1861, 239, 673, 2069, 2083, 317, 73, 599, 571, 191, 631, 1451

Offset

1,1

Comments

From any term back to and including the first, digit by digit, right to left, we can read the resulting primes backwards.

Links

Table of n, a(n) for n=1..53.

Example

a(3) = 11 because 11 is the smallest unused odd prime such that the concatenated reverse terms R(a(3))||R(a(2))||R(a(1)) = 1153 is prime. Trying the smallest unused odd prime 7 fails because 753 = 3*251, a composite number.
a(5) = 29 as its reverse 92 concatenated with the reversed chain of the previous reversed terms 7, 11, 5, 3, gives 9271153, a prime, and no smaller unused odd prime satisfies that condition.

Maple

rev:= proc(n) local L, i; L:= convert(n, base, 10); add(L[-i]*10^(i-1), i=1..nops(L)) end proc:
tcat:= proc(a, b) 10^(1+ilog10(b))*a+b end proc:
Q:= 3: S:= {3}: p:= 3: count:= 1: R:= 3:
while count < 100 do
  q:= p;
  do
    if not member(q, S) then
      rq:= rev(q);
      if isprime(tcat(rq, Q)) then
        count:= count+1;
        R:= R, q;
        Q:= tcat(rq, Q);
        S:= S union {q};
        if q = p then p:= nextprime(p) fi;
        break
      fi;
   fi;
   q:= nextprime(q);
   od;
od:
R; # Robert Israel, Dec 21 2022

Mathematica

a[1] = 3; a[n_] := a[n] = Module[{s = Array[a, n - 1], p = 5}, While[MemberQ[s, p] || ! PrimeQ[FromDigits @ Reverse @ Flatten @ IntegerDigits[Join[s, {p}]]], p = NextPrime[p]]; p]; Array[a, 50] (* Amiram Eldar, Dec 17 2022 *)

Prog

(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    alst, aset, arev, minp = [], set(), "", 3
    while True:
        p = minp
        while p in aset or not isprime(int(str(p)[::-1] + arev)):
            p = nextprime(p)
        yield p; alst.append(p); aset.add(p); arev = str(p)[::-1] + arev
        while minp in aset: minp = nextprime(minp)
print(list(islice(agen(), 53))) # Michael S. Branicky, Dec 16 2022

Crossrefs

Cf. A000040, A004086.

Sequence in context: A087322 A094747 A300783 * A287939 A129738 A271314

Adjacent sequences: A359112 A359113 A359114 * A359116 A359117 A359118

Keyword

nonn,base

Author

Tamas Sandor Nagy, Dec 16 2022

Status

approved