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
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
Programs
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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
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