A114009 Regular triangle where n-th row is composed of n primes beginning with prime(n).

2, 3, 31, 5, 53, 59, 7, 71, 73, 79, 11, 113, 1103, 1109, 1117, 13, 131, 137, 139, 1301, 1303, 17, 173, 179, 1709, 1721, 1723, 1733, 19, 191, 193, 197, 199, 1901, 1907, 1913, 23, 233, 239, 2309, 2311, 2333, 2339, 2341, 2347, 29, 293, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..11325 (rows 1..150)

Example

One prime beginning with 2, followed by the two primes 3, 31 beginning with 3.
Triangle begins:
  2;
  3, 31;
  5, 53, 59;
  7, 71, 73, 79;
  ...

Mathematica

f[n_] := Block[{c = 0, t = {}, p = Prime[n]}, k = PrimePi[p]; lng = Ceiling[Log[10, p]]; While[c < n, q = Prime[k]; If[p == FromDigits@Take[IntegerDigits@q, lng], c++; AppendTo[t, q]]; k++ ]; t]; Array[f, 10] // Flatten (* Robert G. Wilson v, Nov 17 2005 *)

Prog

(Python)
from itertools import count
from sympy import isprime, prime
def row(n):
    if n == 1: return [2]
    pn, c = prime(n), 1; out = [pn]
    for d in count(1):
        pow10 = 10**d
        base = pn * pow10
        for i in range(1, pow10, 2):
            t = base + i
            if isprime(t): out.append(t); c += 1
            if c == n: return out
print([an for r in range(1, 11) for an in row(r)]) # Michael S. Branicky, Jan 19 2023

Crossrefs

Cf. A000040 (first column).

Sequence in context: A048986 A093712 A035514 * A307453 A143665 A074479

Adjacent sequences: A114006 A114007 A114008 * A114010 A114011 A114012

Keyword

base,nonn,tabl

Author

Amarnath Murthy, Nov 12 2005

Extensions

More terms from Robert G. Wilson v, Nov 17 2005

Name clarified by Michel Marcus, Sep 16 2013

Status

approved