A087594 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.).

13, 29, 31, 41, 47, 53, 61, 79, 83, 97, 103, 113, 163, 227, 229, 331, 347, 367, 401, 449, 487, 503, 521, 523, 541, 547, 557, 563, 569, 587, 601, 661, 709, 743, 769, 821, 823, 881, 883, 907, 941, 947, 967, 997, 1063, 1069, 1103, 1163, 1481, 1609, 1621, 1663

Offset

0,1

Comments

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

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Example

29 is a member as absolute(2-9) = 7 is a prime.
347 is a member as dd(347) = 13, dd(13) = 2.

Mathematica

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

Crossrefs

Cf. A087593, A087595.

Sequence in context: A293661 A087593 A158075 * A320868 A347816 A319167

Adjacent sequences: A087591 A087592 A087593 * A087595 A087596 A087597

Keyword

base,nonn

Author

Amarnath Murthy, Sep 18 2003

Extensions

More terms from David Wasserman, Jun 15 2005

Status

approved