A087594 - OEIS

%I #7 Dec 05 2013 19:56:32

%S 13,29,31,41,47,53,61,79,83,97,103,113,163,227,229,331,347,367,401,

%T 449,487,503,521,523,541,547,557,563,569,587,601,661,709,743,769,821,

%U 823,881,883,907,941,947,967,997,1063,1069,1103,1163,1481,1609,1621,1663

%N Define dd(n) = the number formed by concatenating the absolute difference of successive digits. Sequence contains primes p such that dd(p)=q is a prime, dd(q) is also a prime = r and so on until a single-digit prime (2,3,5,7) arises. (Primes in which the number formed by successive digit differences are primes at every step until a single-digit prime is obtained.).

%C Conjecture: Sequence is infinite. Subsidiary sequence: number of n-digit members.

%H Harvey P. Dale, <a href="/A087594/b087594.txt">Table of n, a(n) for n = 0..1000</a>

%e 29 is a member as absolute(2-9) = 7 is a prime.

%e 347 is a member as dd(347) = 13, dd(13) = 2.

%t adsd[n_]:=FromDigits[Abs/@Differences[IntegerDigits[n]]]; Select[Prime[ Range[ 300]], And@@PrimeQ[NestWhileList[adsd,adsd[#],IntegerLength[#]>1&]]&] (* _Harvey P. Dale_, Mar 16 2013 *)

%Y Cf. A087593, A087595.

%K base,nonn

%O 0,1

%A _Amarnath Murthy_, Sep 18 2003

%E More terms from _David Wasserman_, Jun 15 2005