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
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
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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
Comments