A323396 Irregular array read by rows, where T(n, k) is the k-th prime that is both left-truncatable and right-truncatable in base n.

2, 23, 2, 3, 11, 2, 3, 13, 17, 67, 2, 3, 5, 17, 23, 83, 191, 479, 839, 2, 3, 5, 17, 19, 23, 37, 2, 3, 5, 7, 19, 23, 29, 31, 43, 47, 59, 61, 139, 157, 239, 251, 331, 349, 379, 479, 491, 1867, 2, 3, 5, 7, 23, 29, 47, 173, 2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397

Offset: 3

Author

Daniel Suteu and Felix Fröhlich, Jan 13 2019

Keywords

• nonn
• base
• look
• tabf

Comments

The n-th row contains A323390(n) terms.

The largest term in the n-th row is given by A323137(n).

Examples

			Rows for n = 3..7:
  [2, 23]
  [2,  3, 11]
  [2,  3, 13, 17, 67]
  [2,  3,  5, 17, 23, 83, 191, 479, 839]
  [2,  3,  5, 17, 19, 23,  37]
		

Links

• Daniel Suteu, Table of n, a(n) for n = 3..6587
• Wikipedia, Truncatable prime

Crossrefs

Cf. A020994, A076586, A076623, A323137, A323390.

Programs

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));
row(n) = vecsort(bothTruncatablePrimesInBase(n));
T(n,k) = row(n)[k];