cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A108773 Concatenation of n and the sum of the digits of n.

Original entry on oeis.org

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 112, 123, 134, 145, 156, 167, 178, 189, 1910, 202, 213, 224, 235, 246, 257, 268, 279, 2810, 2911, 303, 314, 325, 336, 347, 358, 369, 3710, 3811, 3912, 404, 415, 426, 437, 448, 459, 4610, 4711, 4812, 4913, 505, 516, 527
Offset: 0

Views

Author

N. J. A. Sloane, Jun 26 2005

Keywords

Comments

A136614(n) = A007953(a(n)) = A007953(A136613(n)). - Reinhard Zumkeller, Jan 13 2008

Links

Crossrefs

Cf. A108203, A062028, A064806.
Cf. A007953.

Programs

  • Mathematica
    f[n_] := FromDigits[ Join[ IntegerDigits[n], IntegerDigits[Plus @@ IntegerDigits[n]]]]; Table[ f[n], {n, 0, 52}] (* Robert G. Wilson v, Jun 28 2005 *)
  • PARI
    a(n) = eval(concat(Str(n), Str(sumdigits(n)))); \\ Michel Marcus, Nov 12 2023

Extensions

More terms from Robert G. Wilson v, Jun 28 2005

A308104 Distinct values taken by the DENEAT operator (A073053) in increasing order.

Original entry on oeis.org

11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 112, 123, 134, 145, 156, 167, 178, 189, 202, 213, 224, 235, 246, 257, 268, 279, 303, 314, 325, 336, 347, 358, 369, 404, 415, 426, 437, 448, 459, 505, 516, 527, 538, 549, 606, 617, 628, 639, 707, 718, 729, 808, 819, 909, 1010
Offset: 1

Views

Author

Rémy Sigrist, May 13 2019

Keywords

Comments

This sequence corresponds to numbers of the form e.o.(e+o) with e, o >= 0 and e+o > 0 (where "." denotes concatenation in decimal).
This sequence first differs from A108203 for n = 55: a(55) = 1010 whereas A108203(55) = 1001.

Links

Crossrefs

See A308106 for the values in order of appearance.
Cf. A073053, A108203.

Programs

  • PARI
    See Links section.

A302575 Numbers x which are the concatenation of y and the product of the digits of y.

Original entry on oeis.org

11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 111, 122, 133, 144, 155, 166, 177, 188, 199, 200, 212, 224, 236, 248, 300, 313, 326, 339, 400, 414, 428, 500, 515, 600, 616, 700, 717, 800, 818, 900, 919, 1000, 1010, 1020, 1030, 1040, 1050, 1060, 1070, 1080, 1090, 1100
Offset: 1

Views

Author

Paolo P. Lava, Apr 10 2018

Keywords

Examples

			100 => 1*0 = 0; 326 => 3*2 = 6; 127798 => 1*2*7*7 = 98.

Crossrefs

Cf. A007954, A108203.

Programs

  • Maple
    P:=proc(n) local k, ok; ok:=0; for k from 1 to ilog10(n) do
if convert(convert(trunc(n/10^k), base, 10), `*`)=n mod 10^k then ok:=1; break; fi; od;
if ok=1 then if n<100 or k
  • PARI
    isok(n) = {d = digits(n); for (k=1, #d-1, da = vector(k, i, d[i]); db = vector(#d-k, i, d[k+i]); na = fromdigits(da); nb = fromdigits(db); if ((nb && db[1] != 0) || (nb==0), if (prod(j=1, k, da[j]) == nb, return (1));););} \\ Michel Marcus, Apr 13 2018

A329719 Numbers whose digits can be partitioned into at least 3 segments (not beginning with 0) where each segment is the sum of the previous two segments.

Original entry on oeis.org

112, 123, 134, 145, 156, 167, 178, 189, 213, 224, 235, 246, 257, 268, 279, 314, 325, 336, 347, 358, 369, 415, 426, 437, 448, 459, 516, 527, 538, 549, 617, 628, 639, 718, 729, 819, 1123, 1235, 1347, 1459, 1910, 2134, 2246, 2358, 2810, 2911, 3145, 3257, 3369
Offset: 1

Views

Author

Bi Cheng Wu, Nov 19 2019

Keywords

Examples

			112 -> 1+1=2;
1235 -> 1+2=3 and 2+3=5;
224610 -> 2+2=4 and 2+4=6 and 4+6=10.

Links

Crossrefs

Shares subsequences with A108203, A308104, A214527.
Cf. A019523.

Programs

  • Mathematica
    part[n_] := part[n] = Select[Flatten[ Permutations /@ Reverse /@ IntegerPartitions[n, {3,n}], 1], 0 <= #[[3]] - Max[#[[1]], #[[2]]] <= 1 && AllTrue[Rest@ Rest@ Differences@ #, 0 <= # <= 1 &] &]; spl[x_, L_] := Map[ FromDigits@ Take[x, #] &, Transpose[{Most@ #, Rest[#]-1}& [ FoldList[ Plus, 1, L]]]]; sumQ[w_] := AllTrue[Range[3, Length@w], w[[#]] == w[[#-1]] + w[[#-2]] &]; ok[n_] := Block[{m = IntegerLength@ n}, AnyTrue[ spl[ IntegerDigits[n], #] & /@ part[m], sumQ[#] && Total[ IntegerLength /@ #] == m &]]; Select[ Range[100, 6000], ok] (* Giovanni Resta, Dec 03 2019 *)
  • Python
    def isSegmentSum(digits,segment1=None,segment2=None):
    digits = str(digits)
    N = len(digits)
    if N == 0:
        return True
    else:
        if (segment1 is None) and (segment2 is None):
            for i in range(N):
                try:
                    slice1 = digits[:i+1]
                    for j in range(N-(i+1)):
                        slice2 = digits[i+1:i+1+j+1]
                        slice3 = digits[i+1+j+1:]
                        if (isSegmentSum(slice3,slice1,slice2) and
                         len(slice3)>0 and not (slice1.startswith("0") or
                         slice2.startswith("0") or
                         (slice3.startswith("0")))):
                            return True
                except:
                    return False
        else:
            sumOfDigits = str(int(segment1)+int(segment2))
            nS = len(sumOfDigits)
            try:
                if digits[:nS] == sumOfDigits:
                    return isSegmentSum(digits[nS:],segment2,digits[:nS])
                else:
                    return False
            except:
                return False
    return False
def findSegmentSum(lower,upper):
    for i in range(lower,upper+1):
        if isSegmentSum(i):
            print(str(i))
findSegmentSum(1, 5200)
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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