login
Least Luhn prime in base 2n: primes p such that p + reverse(p) in base 2n is also a prime.
1

%I #25 May 31 2024 22:10:21

%S 2,37,83,137,229,317,409,557,677,829,991,1187,1423,1597,1871,2083,

%T 2347,2633,2939,3307,3581,3967,4297,4673,5051,5479,5927,6343,6791,

%U 7349,7757,8269,8783,9323,9871,10463,11069,11633,12251,12889,13537,14207,14891,15641

%N Least Luhn prime in base 2n: primes p such that p + reverse(p) in base 2n is also a prime.

%C Luhn primes were named after Norman Luhn, who first noted the property of 229 on the website Prime Curios!.

%C There are no Luhn primes in odd base, and only one, 2, in base 2.

%H Amiram Eldar, <a href="/A309429/b309429.txt">Table of n, a(n) for n = 1..1000</a>

%H Octavian Cira and Florentin Smarandache, <a href="http://www.uav.ro/stiinte_exacte/journal/index.php/TAMCS/article/download/112/90">Luhn prime numbers</a>, Theory and Applications of Mathematics & Computer Science, Vol. 5, No. 1 (2015), pp. 1-8.

%H G. L. Honaker, Jr. and Chris Caldwell, eds., <a href="https://primes.utm.edu/curios/page.php?curio_id=2522">229</a>, Prime Curios!, November 19, 2001.

%F a(n) > 8*n^2 for n > 1.

%e a(2) = 37 since 37 = 211 in base 2*2 = 4, and 211+112 = 323 which equals 59 in base 10 and is prime.

%t a[b_] := Module[{p=2}, While[!PrimeQ[p + FromDigits[Reverse @ IntegerDigits[p, b], b]], p = NextPrime[p]]; p]; Table[a[n], {n, 2, 88, 2}]

%o (PARI) a(n) = {my(p=2); while (!isprime(p+fromdigits(Vecrev(digits(p, 2*n)), 2*n)), p = nextprime(p+1)); p;} \\ _Michel Marcus_, Aug 03 2019

%Y Cf. A061783.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Aug 02 2019