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

29, 47, 83, 137, 173, 191, 227, 263, 281, 317, 353, 443, 461, 599, 641, 797, 821, 887, 911, 977, 1019, 1091, 1109, 1163, 1181, 1217, 1307, 1361, 1433, 1451, 1499, 1523, 1613, 1697, 1721, 1787, 1811, 1877, 1901, 1949, 2027, 2063, 2081, 2153, 2207, 2243

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), May 27 2006

Keywords

• base
• nonn

Comments

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.

Examples

			443 is in the sequence because it is the largest number of the prime trio (443, 11, 2).
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
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Luc Stevens, Prime ensembles

Crossrefs

Subsequence of A304367.

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.

Cf. A119889, A119890, A119892.

Programs

Maple

filter:= proc(n) local x,y;
  if not isprime(n) then return false fi;
  x:= convert(convert(n,base,10),`+`);
  if x < 10 or not isprime(x) then return false fi;
  y:= convert(convert(x,base,10),`+`);
  member(y,{2,3,5,7})
end proc:
select(filter, [seq(i,i=11..10000,2)]); # Robert Israel, May 21 2021

Mathematica

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 *)

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