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A342575 a(n) is the exponent of the least power of 2 such that the concatenated digits of the decimal expansion of 2^n are a proper substring of the concatenated digits of the decimal expansion of 2^a(n). 0
4, 5, 6, 7, 14, 15, 26, 102, 103, 104, 224, 103, 104, 105, 506, 507, 452, 1169, 1170, 1171, 8228, 10419, 15186, 5227, 16619, 16620, 16621, 25102, 130090, 62640, 330791, 330792, 351403, 273100, 681504, 649069, 352375, 3045104, 3045105, 3635007, 9532211, 7819691, 3091425, 3091426 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
EXAMPLE
n 2^n a(n) 2^a(n)
0 1 4 _1_6
1 2 5 3_2_
2 4 6 6_4_
3 8 7 12_8_
4 16 14 _16_384
5 32 15 _32_768
6 64 26 671088_64_
7 128 102 50706024009129176059868_128_21504
8 256 103 101412048018258352119736_256_43008
9 512 104 202824096036516704239472_512_86016
10 1024 224 2695994666715 ... 06736371444225405724811036_1024_9216
11 2048 103 10141_2048_01825835211973625643008
12 4096 104 20282_4096_03651670423947251286016
13 8192 105 40564_8192_07303340847894502572032
MAPLE
a:= proc(n) local k, p; p:= ""||(2^n); for k
from n+1 while searchtext(p, ""||(2^k))=0 do od; k
end:
seq(a(n), n=0..24); # Alois P. Heinz, Mar 17 2021
PROG
(Python)
def a(n):
k, twok, target = n+1, 2**(n+1), str(2**n)
while target not in str(twok): k, twok = k+1, twok*2
return k
print([a(n) for n in range(27)]) # Michael S. Branicky, Mar 16 2021
(PARI) vecmatch(vshort, vlong)={my(l=#vshort, L=#vlong); for(i=0, L-l, if(vshort==vlong[i+1..i+l], return(i+1))); 0}
for(n=0, 26, my(vx=digits(2^n)); for(y=n+1, oo, my(vy=digits(2^y)); if(vecmatch(vx, vy)>0, print1(y, ", "); break)))
(PARI) a(n) = my(k=n+1, s=Str(2^n)); while (#strsplit(Str(2^k), s) <=1, k++); k; \\ Michel Marcus, Mar 17 2021
CROSSREFS
Cf. A342601.
Sequence in context: A283775 A037355 A294228 * A046300 A053738 A327101
KEYWORD
nonn,base
AUTHOR
Hugo Pfoertner, Mar 16 2021
EXTENSIONS
a(28)-a(36) from Jon E. Schoenfield, confirmed by Michael S. Branicky, Mar 17 2021
a(37)-a(43) from Bert Dobbelaere, Mar 19 2021
STATUS
approved

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Last modified June 20 23:18 EDT 2024. Contains 373535 sequences. (Running on oeis4.)