A113625 Irregular triangle in which the n-th row contains all primes having digit sum n (not containing the digit '0') in increasing order.

2, 11, 3, 13, 31, 211, 5, 23, 41, 113, 131, 311, 2111, 7, 43, 61, 151, 223, 241, 313, 331, 421, 1123, 1213, 1231, 1321, 2113, 2131, 2221, 2311, 3121, 4111, 11113, 11131, 11311, 12211, 21121, 21211, 22111, 111121, 111211, 112111, 17, 53, 71, 233, 251, 431, 521

Offset: 2

Author

Amarnath Murthy, Nov 10 2005

Keywords

• base
• tabf
• nonn
• look

Comments

The number of primes in the n-th row is A073901(n). The smallest prime in the n-th row is A067180(n). The largest prime in the n-th row is A069869(n).

Examples

			Starting with row 2, the table is
2, 11
3
13, 31, 211
5, 23, 41, 113, 131, 311, 2111
none
7, 43, 61, 151, 223, 241, 313, 331, 421, 1123,...
		

Links

• Alois P. Heinz, Rows n = 2..17, flattened (Rows n = 2..14 from T. D. Noe)

Crossrefs

Cf. A110741 (with contraints on number of digits).

Programs

Maple

with(combinat):
b:= proc(n, i, l) option remember; `if`(n=0, select(isprime,
      map(x-> parse(cat(x[])), permute(l))), `if`(i<1, [],
      [seq(b(n-i*j, i-1, [l[],i$j])[], j=0..n/i)]))
    end:
T:= n-> sort(b(n, 9, []))[]:
seq(T(n), n=2..8);  # Alois P. Heinz, May 25 2013

Mathematica

Table[If[n > 3 && Mod[n, 3] == 0, {}, p = IntegerPartitions[n]; u = {}; Do[t = Permutations[i]; u = Union[u, Select[FromDigits /@ t, PrimeQ]], {i, p}]; u], {n, 2, 14}]

Extensions

Edited, corrected and extended by Stefan Steinerberger, Aug 10 2007

Edited by T. D. Noe, Jan 25 2011