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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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

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

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

LINKS

Daniel Suteu, Table of n, a(n) for n = 3..6587

Wikipedia, Truncatable prime

EXAMPLE

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]

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));

row(n) = vecsort(bothTruncatablePrimesInBase(n));

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

CROSSREFS

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

Sequence in context: A052077 A124604 A329336 * A107801 A262702 A076653

Adjacent sequences:  A323393 A323394 A323395 * A323397 A323398 A323399

KEYWORD

nonn,base,look,tabf

AUTHOR

Daniel Suteu and Felix Fröhlich, Jan 13 2019

STATUS

approved

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Last modified August 11 06:25 EDT 2020. Contains 336422 sequences. (Running on oeis4.)