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A106820
Smallest prime of the set of three consecutive primes whose sum of digits is a set of three distinct primes.
1
2, 3, 5, 41, 131, 191, 193, 223, 311, 317, 397, 461, 593, 599, 641, 821, 823, 881, 1031, 1091, 1093, 1097, 1291, 1297, 1301, 1321, 1327, 1451, 1709, 1871, 2069, 2081, 2083, 2179, 2311, 2351, 2357, 2551, 2557, 2579, 2711, 3163, 3167, 3251, 3253, 3257, 3259
OFFSET
1,1
LINKS
EXAMPLE
a(4)=41 is a term because sum of digits of three consecutive primes i.e. i.e. (41, 43, 47), whose sum of digits (i.e. 5, 7, 11)is a set of three distinct primes.
MATHEMATICA
tdpQ[{a_, b_, c_}]:=Module[{d=Total[IntegerDigits[a]], e=Total[ IntegerDigits[ b]], f=Total[IntegerDigits[c]]}, Length[Union[{d, e, f}]]==3&&AllTrue[ {d, e, f}, PrimeQ]]; Select[Partition[Prime[ Range[ 500]], 3, 1], tdpQ][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 12 2021 *)
CROSSREFS
Sequence in context: A224781 A136015 A106713 * A362957 A042469 A107990
KEYWORD
base,nonn
AUTHOR
Shyam Sunder Gupta, May 18 2005
STATUS
approved