OFFSET
1,1
COMMENTS
If we remove either constraint of q < p or q being prime, then the sequence would be all prime numbers (A000040).
By definition it is a superset of A016041, and is a proper superset by construction (e.g., 13 is in the sequence).
Some terms have multiple bases that yield palindromic representations, the first being 31 (which is palindromic in both base 2 and base 5). The smallest prime p such that there exist n distinct primes less than p that give palindromic representations of p is A372142(n).
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..11371 (terms 1..1000 from Tadayoshi Kamegai)
EXAMPLE
11 is not in this sequence as its representation in base 2 is 1011, in base 3 is 102, in base 5 is 21, in base 7 is 14, none of which are palindromic.
1483 is in this sequence as its representation in base 37 is 131, which is palindromic.
MATHEMATICA
a={}; For[i=1, i<=155, i++, flag=0; For[j=1, Prime[j] < Prime[i] && flag==0, j++, If[PalindromeQ[IntegerDigits[Prime[i], Prime[j]]], flag=1; AppendTo[a, Prime[i]]]]]; a (* Stefano Spezia, Apr 22 2024 *)
PROG
(Python)
from sympy import sieve
from sympy.ntheory import digits
from itertools import islice
def ispal(v): return v == v[::-1]
def agen(): yield from (p for p in sieve if any(ispal(digits(p, q)[1:]) for q in sieve.primerange(1, p)))
print(list(islice(agen(), 60))) # Michael S. Branicky, Apr 20 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Tadayoshi Kamegai, Apr 20 2024
STATUS
approved