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

1,1

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.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Luc Stevens, Prime ensembles

Example

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

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 *)

Prog

(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

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.

Sequence in context: A344466 A102852 A138052 * A106754 A222413 A063642

Adjacent sequences: A119888 A119889 A119890 * A119892 A119893 A119894

Keyword

base,nonn

Author

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

Status

approved