cp's OEIS Frontend

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

%I A113625 #35 May 22 2025 04:41:49
%S A113625 2,11,3,13,31,211,5,23,41,113,131,311,2111,7,43,61,151,223,241,313,
%T A113625 331,421,1123,1213,1231,1321,2113,2131,2221,2311,3121,4111,11113,
%U A113625 11131,11311,12211,21121,21211,22111,111121,111211,112111,17,53,71,233,251,431,521
%N A113625 Irregular triangle in which the n-th row contains all primes having digit sum n (not containing the digit '0') in increasing order.
%C A113625 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).
%H A113625 Alois P. Heinz, <a href="/A113625/b113625.txt">Rows n = 2..17, flattened</a> (Rows n = 2..14 from T. D. Noe)
%e A113625 Starting with row 2, the table is
%e A113625 2, 11
%e A113625 3
%e A113625 13, 31, 211
%e A113625 5, 23, 41, 113, 131, 311, 2111
%e A113625 none
%e A113625 7, 43, 61, 151, 223, 241, 313, 331, 421, 1123,...
%p A113625 with(combinat):
%p A113625 b:= proc(n, i, l) option remember; `if`(n=0, select(isprime,
%p A113625       map(x-> parse(cat(x[])), permute(l))), `if`(i<1, [],
%p A113625       [seq(b(n-i*j, i-1, [l[],i$j])[], j=0..n/i)]))
%p A113625     end:
%p A113625 T:= n-> sort(b(n, 9, []))[]:
%p A113625 seq(T(n), n=2..8);  # _Alois P. Heinz_, May 25 2013
%t A113625 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}]
%Y A113625 Cf. A110741 (with contraints on number of digits).
%K A113625 base,tabf,nonn,look
%O A113625 2,1
%A A113625 _Amarnath Murthy_, Nov 10 2005
%E A113625 Edited, corrected and extended by _Stefan Steinerberger_, Aug 10 2007
%E A113625 Edited by _T. D. Noe_, Jan 25 2011