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 A264117 Largest integer which cannot be partitioned using only parts from the set {perfect powers excluding the n smallest}. 1
 23, 55, 87, 94, 119, 178, 271, 312, 335, 403, 501, 551, 598, 717, 861, 861, 903, 1022, 1119, 1248, 1463, 1535, 1688, 2031, 2067, 2416, 2535, 2976, 3064, 3164, 3407, 3552, 3552, 4023, 4143, 4416, 4633, 4663, 5424, 5424, 5688, 6000, 6455 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It appears, but has not been proved, that for n>28, a(n) < a(n-1) + A001597(n). LINKS Martin Y. Champel, Table of n, a(n) for n = 1..281 EXAMPLE a(1) = 23 as 23 cannot be obtained by any combination of {4, 8, 9, 16} but the 4 following integers can: 24 (6*4) a combination of {4, 8, 9, 16}, 25 (1*25) a combination of {4, 8, 9, 16, 25}, 26 (1*8+2*9) a combination of {4, 8, 9, 16, 25}, 27 (1*27) a combination of {4, 8, 9, 16, 25, 27} so all following integers can. a(2) = 55 as 55 cannot be obtained by any combination of {8, 9, 16, 25, 27, 32, 36, 49} but the 8 following integers can. a(3) = 87 as 87 cannot be obtained by any combination of {9, 16, 25, 27, 32, 36, 49, 64, 81} but the 9 following integers can. PROG (Python 2.7) from copy import * from math import * sol ={} def a(n): ....global sol ....if n in sol: return sol[n] ....k = n**2 + 100 ....yt = sorted(list(set([b**a for a in range(2, 1+int(log(k)/log(2))) for b in range(1, 1+int(k**(1./a)))])))[n:] ....p0 = yt[0] ....if n-1 in sol and n > 28: p1 = sol[n-1] + 2 * p0 ....else: p1 = 7 * p0 + 400 ....yt = sorted(list(set([b**a for a in range(2, 1+int(log(p1)/log(2))) for b in range(1, 1+int(p1**(1./a)))])))[n:] ....st = [] ....while st != yt: ........st = deepcopy(yt) ........yt = sorted(list(set(yt + [i+j for i in yt for j in yt if i>=j if i+j < p1]))) ....d = 0 ....f = yt[0] + 1 ....t = f ....for i in range(1, len(yt)): ........if yt[i] == f: ............d += 1 ............f += 1 ............if d == yt[0] + 1: ................yt = yt[:yt.index(t+1)] ................sol[n] = yt.pop() + 1 ................return sol[n] ........else: ............t = f ............f = yt[i]+1 ............d = 0 CROSSREFS Cf. A001597. Sequence in context: A053236 A118603 A303891 * A033657 A305283 A166144 Adjacent sequences: A264114 A264115 A264116 * A264118 A264119 A264120 KEYWORD nonn AUTHOR Martin Y. Champel, Nov 03 2015 STATUS approved

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Last modified January 28 14:40 EST 2023. Contains 359895 sequences. (Running on oeis4.)