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%I #25 Jan 19 2023 11:02:14
%S 2,3,31,5,53,59,7,71,73,79,11,113,1103,1109,1117,13,131,137,139,1301,
%T 1303,17,173,179,1709,1721,1723,1733,19,191,193,197,199,1901,1907,
%U 1913,23,233,239,2309,2311,2333,2339,2341,2347,29,293,2903,2909,2917,2927,2939,2953,2957,2963
%N Regular triangle where n-th row is composed of n primes beginning with prime(n).
%H Michael S. Branicky, <a href="/A114009/b114009.txt">Table of n, a(n) for n = 1..11325</a> (rows 1..150)
%e One prime beginning with 2, followed by the two primes 3, 31 beginning with 3.
%e Triangle begins:
%e 2;
%e 3, 31;
%e 5, 53, 59;
%e 7, 71, 73, 79;
%e ...
%t 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 *)
%o (Python)
%o from itertools import count
%o from sympy import isprime, prime
%o def row(n):
%o if n == 1: return [2]
%o pn, c = prime(n), 1; out = [pn]
%o for d in count(1):
%o pow10 = 10**d
%o base = pn * pow10
%o for i in range(1, pow10, 2):
%o t = base + i
%o if isprime(t): out.append(t); c += 1
%o if c == n: return out
%o print([an for r in range(1, 11) for an in row(r)]) # _Michael S. Branicky_, Jan 19 2023
%Y Cf. A000040 (first column).
%K base,nonn,tabl
%O 1,1
%A _Amarnath Murthy_, Nov 12 2005
%E More terms from _Robert G. Wilson v_, Nov 17 2005
%E Name clarified by _Michel Marcus_, Sep 16 2013
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