A172983 Partial sums of near-repdigit primes A056710.

113, 312, 523, 746, 973, 1202, 1435, 1712, 2023, 2354, 2691, 3124, 3567, 4016, 4515, 5072, 5649, 6248, 6909, 7586, 8319, 9092, 9903, 10780, 11661, 12544, 13431, 14342, 15319, 16310, 17307, 18424, 20201, 22200, 24311, 26532, 28865, 31642, 34641, 37972, 42083

Offset

1,1

Comments

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?

Links

Table of n, a(n) for n=1..41.

Formula

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}.

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A000040, A056710.

Sequence in context: A031932 A216310 A211445 * A358034 A069794 A033249

Adjacent sequences: A172980 A172981 A172982 * A172984 A172985 A172986

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Feb 06 2010

Extensions

Corrected and extended by Harvey P. Dale, Apr 07 2013

Status

approved