A178137 Partial sums of A068148.

2, 5, 10, 17, 28, 51, 94, 161, 250, 351, 460, 671, 894, 1127, 1560, 2003, 2680, 3467, 4344, 5231, 6240, 7349, 8472, 9695, 11806, 14027, 16360, 19581, 22904, 26247, 29680, 34247, 39690, 47479, 55356, 64243, 73242, 82243, 91254, 101141, 111042

Offset

1,1

Comments

Partial sums of primes in which neighboring digits differ at most by 1 (neighbors of 9 are 0 and 8 and 9). The subsequence of primes in this partial sum begins: 5, 17, 2003, 3467, 5231, 7349, 101141, 187367. What is the smallest value in this partial sum (after 5) which is itself a prime in which neighboring digits differ at most by 1? What is the analog in other bases?

Links

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

Formula

a(n) = SUM[i=1..n] A068148(i).

Example

a(16) = 2 + 3 + 5 + 7 + 11 + 23 + 43 + 67 + 89 + 101 + 109 + 211 + 223 + 233 + 433 + 443 = 2003 is prime.

Mathematica

Accumulate[Select[Prime[Range[1500]], Max[Abs[Differences[ IntegerDigits[ #]]] /.{9->1}] <2&]] (* Harvey P. Dale, Apr 01 2019 *)

Crossrefs

Cf. A000040, A007504 - Sum of first n primes, A068148.

Sequence in context: A011894 A172512 A172982 * A071602 A046485 A294562

Adjacent sequences: A178134 A178135 A178136 * A178138 A178139 A178140

Keyword

base,easy,nonn

Author

Jonathan Vos Post, May 20 2010

Status

approved