A106820 Smallest prime of the set of three consecutive primes whose sum of digits is a set of three distinct primes.

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Adjacent sequences: A106817 A106818 A106819 * A106821 A106822 A106823

Keyword

base,nonn

Author

Shyam Sunder Gupta, May 18 2005

Status

approved