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

2,1

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).

Links

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

Example

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,...

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}]

Crossrefs

Sequence in context: A275536 A060002 A110741 * A279237 A090323 A127668

Adjacent sequences: A113622 A113623 A113624 * A113626 A113627 A113628

Keyword

base,tabf,nonn,look

Author

Amarnath Murthy, Nov 10 2005

Extensions

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

Edited by T. D. Noe, Jan 25 2011

Status

approved