A308104 -id:A308104 - cp's OEIS frontend

A308106 Distinct values taken by the DENEAT operator (A073053) in order of appearance.

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

Offset: 1

Rémy Sigrist, May 13 2019

			A073053 starts:       101, 11, 101, 11, 101, 11, 101, 11, 101, 11, 112, 22, ...
This sequence starts: 101, 11,                                     112, 22, ...

Rémy Sigrist, PARI program for A308106

See A308104 for the values in increasing order.

Cf. A073053.

PARI
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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

Bi Cheng Wu, Nov 19 2019

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

Bi Cheng Wu, Table of n, a(n) for n = 1..4958 (a(n) < 1000000)

Shares subsequences with A108203, A308104, A214527.

Cf. A019523.

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 *)

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)

cp's OEIS Frontend

A308106 Distinct values taken by the DENEAT operator (A073053) in order of appearance.

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