A172463 - OEIS

%I #5 Nov 21 2013 12:49:59

%S 13,30,61,98,169,242,321,418,525,638,787,944,1111,1290,1489,1800,2137,

%T 2484,2843,3232,3933,4642,5375,6114,6857,7608,8369,9138,10045,10982,

%U 11923,12876,13843,14814,15797,16788,17797,18818,19849,20882

%N Partial sums of emirps, primes whose reversal is a different prime (A006567).

%C The subsequence of prime partial sums of emirps begins: 13, xxx, 787, 1489, 2137, 2843, 3232, 6857, 8369, 11923, 15797, 21943, 24103. The subsubsequence of emirp partial sums of emirps begins: 13, 32911 = emirp(736). Note that 787 is a prime when reversed, but not a different prime. The first square in the sequence is 169 and R(169) = 961 is also a square.

%H Harvey P. Dale, <a href="/A172463/b172463.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = SUM[i=1..n] {p such that p is prime and R(p) is prime} = SUM[i=1..n] {p such that p is in A000040 and A004086(p) is prime}.

%e a(x) = 13 + 17 + 31 + 37 + 71 + 73 + 79 + 97 + 107 + 113 + 149 + 157 + 167 + 179 + 199 + 311 + 337 + 347 + 359 + 389 + 701 + 709 + 733 + 739 + 743 + 751 + 761 + 769 + 907 + 937 + 941 = 11923, which is prime, and note that R(11923) = 32911 is also prime.

%t emirpQ[n_]:=Module[{idn=IntegerDigits[n],ridn},ridn=Reverse[idn];idn!= ridn && PrimeQ[FromDigits[ridn]]]; Accumulate[Select[Prime[ Range[ 200]], emirpQ]] (* _Harvey P. Dale_, Oct 25 2011 *)

%Y Cf. A000040, A003684, A007628, A046732, A048051, A048052, A048053, A048054, A048895.

%K base,easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Feb 03 2010

%E Corrected by Harvey P. Dale, Oct 25 2011