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%I #33 Oct 27 2023 19:17:00
%S 2,11,3,13,31,211,5,23,41,113,131,311,2111,7,43,61,151,223,241,313,
%T 331,421,1123,1213,1231,1321,2113,2131,2221,2311,3121,4111,11113,
%U 11131,11311,12211,21121,21211,22111,111121,111211,112111,17,53,71,233,251,431,521
%N Irregular triangle in which the n-th row contains all primes having digit sum n (not containing the digit '0') in increasing order.
%C 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 Alois P. Heinz, <a href="/A113625/b113625.txt">Rows n = 2..17, flattened</a> (Rows n = 2..14 from T. D. Noe)
%e Starting with row 2, the table is
%e 2, 11
%e 3
%e 13, 31, 211
%e 5, 23, 41, 113, 131, 311, 2111
%e none
%e 7, 43, 61, 151, 223, 241, 313, 331, 421, 1123,...
%p with(combinat):
%p b:= proc(n, i, l) option remember; `if`(n=0, select(isprime,
%p map(x-> parse(cat(x[])), permute(l))), `if`(i<1, [],
%p [seq(b(n-i*j, i-1, [l[],i$j])[], j=0..n/i)]))
%p end:
%p T:= n-> sort(b(n, 9, []))[]:
%p seq(T(n), n=2..8); # _Alois P. Heinz_, May 25 2013
%t 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}]
%K base,tabf,nonn,look
%O 2,1
%A _Amarnath Murthy_, Nov 10 2005
%E Edited, corrected and extended by _Stefan Steinerberger_, Aug 10 2007
%E Edited by _T. D. Noe_, Jan 25 2011
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