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%I #32 Jan 15 2023 18:38:02
%S 29,47,83,137,173,191,227,263,281,317,353,443,461,599,641,797,821,887,
%T 911,977,1019,1091,1109,1163,1181,1217,1307,1361,1433,1451,1499,1523,
%U 1613,1697,1721,1787,1811,1877,1901,1949,2027,2063,2081,2153,2207,2243
%N Prime trio leaders: largest number of a prime trio.
%C A prime trio is a set of three distinct prime numbers such that the third number is a 1-digit number which is the sum of the digits of the second number and the second number is the sum of the digits of the first number.
%H Robert Israel, <a href="/A119891/b119891.txt">Table of n, a(n) for n = 1..10000</a>
%H Luc Stevens, <a href="http://www.lucstevens.com/Primeensembles.htm">Prime ensembles</a>
%e 443 is in the sequence because it is the largest number of the prime trio (443, 11, 2).
%e 599 is the first term with sum of digits different from 11 (cf. A106754), namely 23 (cf. A106762). This sequence contains also all primes with sum of digits equal to 41, 43, 61 etc., but not 29, 47, ... since the second digit sum must be a single-digit prime, i.e., 2, 3, 5 or 7. - _M. F. Hasler_, Mar 09 2022
%p filter:= proc(n) local x,y;
%p if not isprime(n) then return false fi;
%p x:= convert(convert(n,base,10),`+`);
%p if x < 10 or not isprime(x) then return false fi;
%p y:= convert(convert(x,base,10),`+`);
%p member(y,{2,3,5,7})
%p end proc:
%p select(filter, [seq(i,i=11..10000,2)]); # _Robert Israel_, May 21 2021
%t ptQ[n_]:=Module[{c=NestList[Total[IntegerDigits[#]]&,n,2]},Length[ Union[c]] == 3&&And@@PrimeQ[c]]; Select[Prime[Range[500]],ptQ] (* _Harvey P. Dale_, Aug 15 2012 *)
%o (PARI) select( {is_A119891(n, s=sumdigits(n))=bittest(172, sumdigits(s)) && isprime(s) && s>9 && isprime(n)}, primes([1,2345])) \\ _M. F. Hasler_, Mar 09 2022
%Y Subsequence of A304367.
%Y Cf. A000040 (primes), A007953 (sum of digits), A106754 (primes with s.o.d. = 11), A106762 (s.o.d.(p) = 23), A106774 (s.o.d.(p) = 41), A106775 (s.o.d.(p) = 43), A106787 (s.o.d.(p) = 61): subsequences.
%Y Cf. A119889, A119890, A119892.
%K base,nonn
%O 1,1
%A Luc Stevens (lms022(AT)yahoo.com), May 27 2006
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