A323390 Total number of primes that are both left-truncatable and right-truncatable in base n.

0, 2, 3, 5, 9, 7, 22, 8, 15, 6, 35, 11, 37, 17, 22, 12, 69, 12, 68, 18, 44, 13, 145, 16, 47, 20, 77, 13, 291, 15, 89, 27, 74, 20, 241, 18, 106, 25, 134, 15, 450, 23, 144, 33, 131, 24, 491, 27, 235, 29, 187, 23, 575, 30, 218, 31, 183, 25, 1377, 26, 247, 37, 231

Offset

2,2

Links

Table of n, a(n) for n=2..64.

Chris Caldwell, right-truncatable prime, The Prime Glossary.

Eric Weisstein's World of Mathematics, Truncatable Prime

Example

For n = 2, there are no both-truncatable primes, therefore a(2) = 0.
For n = 3, there are 2 both-truncatable primes: 2, 23.
For n = 4, there are 3 both-truncatable primes: 2, 3, 11.
For n = 5, there are 5 both-truncatable primes: 2, 3, 13, 17, 67.
For n = 6, there are 9 both-truncatable primes: 2, 3, 5, 17, 23, 83, 191, 479, 839.

Prog

(PARI)
digitsToNum(d, base) = sum(k=1, #d, base^(k-1) * d[k]);
isLeftTruncatable(d, base) = my(ok=1); for(k=1, #d, if(!isprime(digitsToNum(d[1..k], base)), ok=0; break)); ok;
generateFromPrefix(p, base) = my(seq = [p]); for(n=1, base-1, my(t=concat(n, p)); if(isprime(digitsToNum(t, base)), seq=concat(seq, select(v -> isLeftTruncatable(v, base), generateFromPrefix(t, base))))); seq;
bothTruncatablePrimesInBase(base) = my(t=[]); my(P=primes(primepi(base-1))); for(k=1, #P, t=concat(t, generateFromPrefix([P[k]], base))); vector(#t, k, digitsToNum(t[k], base));
a(n) = #(bothTruncatablePrimesInBase(n));

Crossrefs

Cf. A020994, A076623, A076586, A323137, A323396.

Sequence in context: A069805 A123923 A045965 * A346096 A324886 A277332

Adjacent sequences: A323387 A323388 A323389 * A323391 A323392 A323393

Keyword

nonn,base

Author

Daniel Suteu, Jan 13 2019

Status

approved