A172983 - OEIS

%I #9 Apr 08 2013 12:03:28

%S 113,312,523,746,973,1202,1435,1712,2023,2354,2691,3124,3567,4016,

%T 4515,5072,5649,6248,6909,7586,8319,9092,9903,10780,11661,12544,13431,

%U 14342,15319,16310,17307,18424,20201,22200,24311,26532,28865,31642,34641,37972,42083

%N Partial sums of near-repdigit primes A056710.

%C The subsequence of prime partial sums of near-repdigit primes begins 113, 523, 14143. What is the smallest near-repdigit prime partial sums of near-repdigit primes?

%F a(n) = SUM[i=1..n] A056710 = SUM[i=1..n] {primes in whose base 10 representation all digits are equal except for an end-digit}.

%e a(3) = 113 + 199 + 211 = 523 is prime. a(20) = 113 + 199 + 211 + 223 + 227 + 229 + 233 + 277 + 311 + 331 + 337 + 433 + 443 + 449 + 499 + 557 + 577 + 599 + 661 + 677.

%t nrdQ[n_]:=Module[{idn=IntegerDigits[n],a,b},a=First[idn];b=Last[idn]; a!=b &&Union[idn]==Sort[{a,b}]]; Accumulate[Select[Prime[Range[26,700]],nrdQ]] (* _Harvey P. Dale_, Apr 07 2013 *)

%Y Cf. A000040, A056710.

%K base,easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Feb 06 2010

%E Corrected and extended by _Harvey P. Dale_, Apr 07 2013