A309429 Least Luhn prime in base 2n: primes p such that p + reverse(p) in base 2n is also a prime.

2, 37, 83, 137, 229, 317, 409, 557, 677, 829, 991, 1187, 1423, 1597, 1871, 2083, 2347, 2633, 2939, 3307, 3581, 3967, 4297, 4673, 5051, 5479, 5927, 6343, 6791, 7349, 7757, 8269, 8783, 9323, 9871, 10463, 11069, 11633, 12251, 12889, 13537, 14207, 14891, 15641

Offset

1,1

Comments

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

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Octavian Cira and Florentin Smarandache, Luhn prime numbers, Theory and Applications of Mathematics & Computer Science, Vol. 5, No. 1 (2015), pp. 1-8.

G. L. Honaker, Jr. and Chris Caldwell, eds., 229, Prime Curios!, November 19, 2001.

Formula

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

Example

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

Mathematica

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}]

Prog

(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

Crossrefs

Cf. A061783.

Sequence in context: A055031 A041161 A106947 * A374919 A258896 A262182

Adjacent sequences: A309426 A309427 A309428 * A309430 A309431 A309432

Keyword

nonn,base

Author

Amiram Eldar, Aug 02 2019

Status

approved