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A119891 Prime trio leaders: largest number of a prime trio.

%I A119891 #32 Jan 15 2023 18:38:02
%S A119891 29,47,83,137,173,191,227,263,281,317,353,443,461,599,641,797,821,887,
%T A119891 911,977,1019,1091,1109,1163,1181,1217,1307,1361,1433,1451,1499,1523,
%U A119891 1613,1697,1721,1787,1811,1877,1901,1949,2027,2063,2081,2153,2207,2243
%N A119891 Prime trio leaders: largest number of a prime trio.
%C A119891 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 A119891 Robert Israel, <a href="/A119891/b119891.txt">Table of n, a(n) for n = 1..10000</a>
%H A119891 Luc Stevens, <a href="http://www.lucstevens.com/Primeensembles.htm">Prime ensembles</a>
%e A119891 443 is in the sequence because it is the largest number of the prime trio (443, 11, 2).
%e A119891 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 A119891 filter:= proc(n) local x,y;
%p A119891   if not isprime(n) then return false fi;
%p A119891   x:= convert(convert(n,base,10),`+`);
%p A119891   if x < 10 or not isprime(x) then return false fi;
%p A119891   y:= convert(convert(x,base,10),`+`);
%p A119891   member(y,{2,3,5,7})
%p A119891 end proc:
%p A119891 select(filter, [seq(i,i=11..10000,2)]); # _Robert Israel_, May 21 2021
%t A119891 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 A119891 (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 A119891 Subsequence of A304367.
%Y A119891 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 A119891 Cf. A119889, A119890, A119892.
%K A119891 base,nonn
%O A119891 1,1
%A A119891 Luc Stevens (lms022(AT)yahoo.com), May 27 2006