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Primes for which only one iteration of 'Prime plus its digit sum equals a prime' is possible.
8

%I #14 Nov 09 2018 21:13:12

%S 13,19,37,53,71,73,97,103,127,163,181,233,271,307,383,389,431,433,499,

%T 509,563,587,631,701,743,787,811,857,859,947,1009,1049,1061,1087,1153,

%U 1171,1223,1283,1423,1483,1489,1553,1597,1601,1607,1733,1801,1861,1867

%N Primes for which only one iteration of 'Prime plus its digit sum equals a prime' is possible.

%C Sequence A048519 lists the primes for which at least (rather than exactly) one iteration of A062028 is "possible". See A048524 .. A048527 and A320878 .. A320880 for further subsequences, and A090009 for the list of their initial terms, starting chains of length >= 3 .. 9. - _M. F. Hasler_, Nov 09 2018

%H Harvey P. Dale, <a href="/A048523/b048523.txt">Table of n, a(n) for n = 1..1000</a>

%e prime 1999 -> 1999 + (1+9+9+9) = prime 2027 -> next iteration yields composite 2038.

%t ppd1Q[n_]:=PrimeQ[Rest[NestList[#+Total[IntegerDigits[#]]&,n,2]]] == {True,False}; Select[Prime[Range[300]],ppd1Q] (* _Harvey P. Dale_, Nov 10 2011 *)

%Y Cf. A047791, A048519.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, May 15 1999