

A172463


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


1



13, 30, 61, 98, 169, 242, 321, 418, 525, 638, 787, 944, 1111, 1290, 1489, 1800, 2137, 2484, 2843, 3232, 3933, 4642, 5375, 6114, 6857, 7608, 8369, 9138, 10045, 10982, 11923, 12876, 13843, 14814, 15797, 16788, 17797, 18818, 19849, 20882
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OFFSET

1,1


COMMENTS

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.


LINKS



FORMULA

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}.


EXAMPLE

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.


MATHEMATICA

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 *)


CROSSREFS



KEYWORD

base,easy,nonn


AUTHOR



EXTENSIONS

Corrected by Harvey P. Dale, Oct 25 2011


STATUS

approved



