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A330653 The prime numbers whose digit sum, adjacent digit sum concatenation, and adjacent digit difference concatenation are also primes.

%I A330653 #17 Jan 08 2020 05:10:51
%S A330653 29,41,47,61,83,101,263,281,401,463,601,607,661,809,821,863,1129,1303,
%T A330653 2063,2267,3121,3181,3301,3343,4001,4603,5309,5581,6007,6043,6803,
%U A330653 6863,7129,7309,8009,8681,8821,9721,9967,10903,10909,14143,16903,17209,18521,19421,20063,20201,20407,20807,21143,24281,25147
%N A330653 The prime numbers whose digit sum, adjacent digit sum concatenation, and adjacent digit difference concatenation are also primes.
%C A330653 This sequence lists the prime numbers whose digit sum A007953, concatenation of adjacent digit sums A053392, and concatenation of adjacent digit differences A040115, are also primes. Due to the digit sum being prime this is a subsequence of A046704.
%C A330653 For primes up to ten million there are 2268 entries, which is about one prime in every 293. The largest digit sum is 53 for a(1482) = 5986889, the largest adjacent digit sum concatenation is 171818141113 for a(2076) = 8999567, and the largest adjacent digit difference concatenation is 993247 for a(2099) = 9096481.
%H A330653 Giovanni Resta, <a href="/A330653/b330653.txt">Table of n, a(n) for n = 1..10000</a>
%H A330653 Chris K. Caldwell, <a href="https://primes.utm.edu/howmany.html">How many primes are there?</a>
%e A330653 a(1) = 29, as 2 + 9 = 11, '2 + 9' = 11, '|2 - 9|' = 7, and 29, 11, 7 are all prime.
%e A330653 a(7) = 263, as 2 + 6 + 3 = 11, '2 + 6' + '6 + 3' = 89, '|2 - 6|' + '|6 - 3|' = 43, and 263, 11, 89, 43 are all prime.
%e A330653 a(25) = 4001, as 4 + 0 + 0 + 1 = 5, '4 + 0' + '0 + 0' + '0 + 1' = 401, '|4 - 0|' + '|0 - 0|' + '|0 - 1|' = 401, and 4001, 5, 401 are all prime.
%Y A330653 Cf. A000040, A007953, A040115, A053392, A046704.
%K A330653 nonn,base
%O A330653 1,1
%A A330653 _Scott R. Shannon_, Dec 22 2019