A172463 Partial sums of emirps, primes whose reversal is a different prime (A006567).

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

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

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

Sequence in context: A048450 A216193 A139577 * A329950 A183445 A296124

Adjacent sequences: A172460 A172461 A172462 * A172464 A172465 A172466

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Feb 03 2010

Extensions

Corrected by Harvey P. Dale, Oct 25 2011

Status

approved