A068148 -id:A068148 - cp's OEIS frontend

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

Jonathan Vos Post, May 20 2010

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?

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

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

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

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

A032981 Positive numbers with the property that all pairs of consecutive base-10 digits differ by 0 or 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23, 32, 33, 34, 43, 44, 45, 54, 55, 56, 65, 66, 67, 76, 77, 78, 87, 88, 89, 98, 99, 100, 101, 110, 111, 112, 121, 122, 123, 210, 211, 212, 221, 222, 223, 232, 233, 234, 321, 322, 323, 332, 333, 334, 343, 344, 345

Offset: 1

Clark Kimberling

a(n) = A178403(n+1) for n < 38. - Reinhard Zumkeller, May 27 2010

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A068148 (primes).

a032981 n = a032981_list !! (n-1)
a032981_list = map read $ filter f $ map show [1..] :: [Int] where
   f ps = all (`elem` neighbours) $ zipWith ((. return) . (:)) ps (tail ps)
   neighbours = "09" : "90" : zipWith ((. return) . (:))
      (digs ++ tail digs ++ init digs) (digs ++ init digs ++ tail digs)
   digs = "0123456789"
-- Reinhard Zumkeller, Feb 14 2015

okQ[n_]:=Max[Abs[Last[#]-First[#]]&/@Partition[IntegerDigits[n],2,1]]<2
Select[Range[350],okQ]  (* Harvey P. Dale, Feb 14 2011 *)

A376425 Numbers whose adjacent digits differ by at most 1 modulo 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23, 32, 33, 34, 43, 44, 45, 54, 55, 56, 65, 66, 67, 76, 77, 78, 87, 88, 89, 90, 98, 99, 100, 101, 109, 110, 111, 112, 121, 122, 123, 210, 211, 212, 221, 222, 223, 232, 233, 234, 321, 322, 323, 332, 333, 334, 343, 344, 345, 432

Offset: 1

Andrew Howroyd, Sep 22 2024

Neighbors of 9 are 0 and 8.

Except for the initial zero this is a strict subsequence of A252490 which uses the same neighborhood rule for digits but considers an unordered set of digits. The first difference is that 102 is included by A252490 but excluded here.

			11 is a term because 1 = 1.
32 is a terms because 3 is a neighbor of 2.
109 is a term because 1 is a neighbor of 0 and 0 is a neighbor of 9 (modulo 10).
121 is a term because 1 is a neighbor of 2 and 2 is a neighbor of 1.

Subsequence of A252490 union {0}.

Cf. A068148, A068149, A087553.

f:= proc(n) local i;
   seq(10*n+i,i= sort([n-1,n,n+1] mod 10))
end proc:
S:= [$1..9]: R:= 0,op(S):
for i from 1 to 3 do
  S:= map(f,S); R:= R,op(S)
od:
R; # Robert Israel, Sep 22 2024

isok(k)={my(v=digits(k)); for(i=2, #v, my(t=abs(v[i]-v[i-1])); if(t>1&&t<9, return(0))); 1}

From Robert Israel, Sep 22 2024 (Start):
Let a(n) mod 10 = d.
If 1 <= d <= 8 then a(3 n + 6 + j) = 10 a(n) + d + j for j = -1, 0, 1.
If d = 0 and n > 1, then a(3 n + 5) = 10 a(n), a(3 n + 6) = 10 a(n) + 1, a(3 n + 7) = 10 a(n) + 9.
If d = 9, then a(3 n + 5) = 10 a(n), a(3 n + 6) = 10 a(n) + 8, a(3 n + 7) = 10 a(n) + 9.
(End)

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A178137 Partial sums of A068148.

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A032981 Positive numbers with the property that all pairs of consecutive base-10 digits differ by 0 or 1.

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A376425 Numbers whose adjacent digits differ by at most 1 modulo 10.

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