A395344 a(n) is the integer obtained by inserting the sum (modulo 10) of adjacent digits of n between them.

1, 2, 3, 4, 5, 6, 7, 8, 9, 110, 121, 132, 143, 154, 165, 176, 187, 198, 109, 220, 231, 242, 253, 264, 275, 286, 297, 208, 219, 330, 341, 352, 363, 374, 385, 396, 307, 318, 329, 440, 451, 462, 473, 484, 495, 406, 417, 428, 439, 550, 561, 572, 583, 594

Offset

1,2

Links

Vincenzo Manto, Table of n, a(n) for n = 1..10000

Example

Letting | denote the concatenation of digits:
   a(10) = 1 | (1 + 0) | 0 = 110,
   a(36) = 3 | (3 + 6) | 6 = 396,
   a(47) = 4 | (4 + 7) mod 10 | 7 = 4 | 1 | 7 = 417,
  a(159) = 1 | (1 + 5) | 5 | (5 + 9) mod 10 | 9 = 16549.

Mathematica

a[n_]:=Module[{d=IntegerDigits[n]}, l=Length[d]; If[l==1, n, Do[j=2i; d=Insert[d, Mod[d[[j-1]]+d[[j]], 10], j], {i, l-1}]; FromDigits[d]]]; Array[a, 54] (* James C. McMahon, Apr 25 2026 *)

Prog

(Python)
def a(n):
    s = str(n)
    if len(s) < 2: return n
    res = []
    for i in range(len(s) - 1):
        d1, d2 = int(s[i]), int(s[i+1])
        res.append(s[i])
        res.append(str((d1 + d2) % 10))
    res.append(s[-1])
    return int("".join(res))
print([a(n) for n in range(1, 55)])

Crossrefs

Cf. A007953, A053837.

Sequence in context: A181352 A056143 A106003 * A283868 A087995 A082232

Adjacent sequences: A395341 A395342 A395343 * A395345 A395346 A395347

Keyword

nonn,base,easy,look

Author

Vincenzo Manto, Apr 20 2026

Status

approved