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A113613 Beginning with 7, distinct primes such that every partial concatenation is a palindrome. 2

%I #8 Aug 10 2022 07:40:26

%S 7,17,5717,27175717,212717571727175717,

%T 8717571727175717212717571727175717,

%U 2327175717271757172127175717271757178717571727175717212717571727175717

%N Beginning with 7, distinct primes such that every partial concatenation is a palindrome.

%C From _Michael S. Branicky_, Aug 09 2022: (Start)

%C If terms were not required to be distinct, then 7, 7, 7, ... or 7, 17, 17, 17, ... satisfy the requirement.

%C a(11) has 1132 digits. (End)

%H Michael S. Branicky, <a href="/A113613/b113613.txt">Table of n, a(n) for n = 1..10</a>

%e 7, 717, 7175717, 717571727175717, ... are all palindromes.

%o (Python)

%o from sympy import isprime

%o from itertools import count, islice, product

%o def pals(digs):

%o yield from digs

%o for d in count(2):

%o for p in product(digs, repeat=d//2):

%o left = "".join(p)

%o for mid in [[""], digs][d%2]:

%o yield left + mid + left[::-1]

%o def folds(s): # generator of suffixes of palindromes starting with s

%o for i in range((len(s)+1)//2, len(s)+1):

%o for mid in [True, False]:

%o t = s[:i] + (s[:i-1][::-1] if mid else s[:i][::-1])

%o if t.startswith(s):

%o yield t[len(s):]

%o yield from ("".join(p)+s[::-1] for p in pals("0123456789"))

%o def agen():

%o s, seen = "7", {"7"}; yield 7

%o while True:

%o for t in folds(s):

%o if len(t) and t[0] != "0" and t not in seen and isprime(int(t)):

%o break

%o s += t; seen.add(t); yield int(t)

%o print(list(islice(agen(), 7))) # _Michael S. Branicky_, Aug 09 2022

%Y Cf. A113612.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Nov 09 2005

%E Name clarified and a(5) and beyond from _Michael S. Branicky_, Aug 09 2022

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Last modified February 29 02:52 EST 2024. Contains 370401 sequences. (Running on oeis4.)