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Initial, all intermediate and final iterated sums of digits of n are primes.
2

%I #11 Jun 13 2014 04:50:16

%S 2,3,5,7,11,12,14,16,20,21,23,25,29,30,32,34,38,41,43,47,50,52,56,61,

%T 65,70,74,83,92,101,102,104,106,110,111,113,115,119,120,122,124,128,

%U 131,133,137,140,142,146,151,155,160,164,173,182,191,200,201,203,205,209,210,212,214,218

%N Initial, all intermediate and final iterated sums of digits of n are primes.

%C 2999 = A062802(4) is the smallest term of this sequence for which the second iterated sum of digits is not the final sum; i.e. the smallest requiring three summations (2+9+9+9=29, 2+9=11, 1+1=2 and all three sums are prime). (The corresponding statement about the very large A062802(5) is not true because a large number of smaller nonprimes of the same digit length also have the digit sum 2999, the least being 29999..., where 333 9's follow the 2.). A062802, a sequence of primes, is a subsequence of this sequence and of A070027.

%C Additional terms can be generated by finding the next number whose digit sum is a prime already in the sequence. - _Felix Fröhlich_, Jun 13 2014

%H Alois P. Heinz, <a href="/A070026/b070026.txt">Table of n, a(n) for n = 1..1000</a>

%e 47 is here because 4+7=11 and 11 is prime while also 1+1=2 and 2 is prime. 39 (in A028835) is not a term: 3+9=12 is not prime - although 1+2=3 is prime. 49 (in A028834) is not a term: 4+9=13 is prime but 1+3=4 is not prime.

%Y Cf. A028834 (Initial sum is prime), A028835 (Final sum is prime), A062802, A070027 (Primes from this sequence).

%K base,easy,nonn

%O 1,1

%A _Rick L. Shepherd_, Apr 13 2002

%E Terms corrected by _Felix Fröhlich_, Jun 13 2014