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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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Bi Cheng Wu, Table of n, a(n) for n = 1..4958 (a(n) < 1000000) EXAMPLE 112 -> 1+1=2; 1235 -> 1+2=3 and 2+3=5; 224610 -> 2+2=4 and 2+4=6 and 4+6=10. 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 *) PROG (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) CROSSREFS Shares subsequences with A108203, A308104, A214527. Cf. A019523. Sequence in context: A036301 A117723 A359142 * A157662 A340125 A095615 Adjacent sequences: A329716 A329717 A329718 * A329720 A329721 A329722 KEYWORD nonn,base AUTHOR Bi Cheng Wu, Nov 19 2019 STATUS approved

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Last modified June 19 10:38 EDT 2024. Contains 373501 sequences. (Running on oeis4.)