A046835
Internal digits of n^2 include digits of n as subsequence, n does not end in 0.
Original entry on oeis.org
3628, 3792, 8882, 14651, 28792, 36574, 37026, 37028, 37073, 58808, 68323, 71213, 75884, 75887, 75888, 87073, 88526, 88796, 88808, 94682, 105125, 105153, 146308, 161574, 269622, 368323, 369255, 369482, 369863, 370137, 370156, 370162, 370178
Offset: 1
From _David A. Corneth_, Aug 29 2023: (Start)
3628 is in the sequence as 3628^2 = 13162384 and so 3628 is in the internal digits; 1(3)1(6)(2)3(8)4, reading from left to right the digits in brackets are 3628 and all these digits are internal digits of 13162384.
1011 is NOT in the seuence as 1011^2 = 1022121 and so 1011 is in the digits;
(1)(0)22(1)2(1) but not all these digits are internal digits of 1022121. (End)
Cf.
A046827,
A046828,
A046829,
A046830,
A046831,
A046832,
A046833,
A046834,
A046835,
A046836,
A046837,
A046838.
-
from itertools import count, islice
def A046835_gen(startvalue=1): # generator of terms >= startvalue
for k in count(max(startvalue,1)):
if k%10:
c = iter(str(k**2)[1:-1])
if all(map(lambda b:any(map(lambda a:a==b,c)),str(k))):
yield k
A046835_list = list(islice(A046835_gen(),20)) # Chai Wah Wu, Apr 03 2023
A383640
Internal digits of k^3 include digits of k as substring, k does not end in 0.
Original entry on oeis.org
56, 782, 5111, 8089, 8216, 9553, 11768, 14357, 18229, 53257, 64164, 65137, 72556, 98442, 213405, 271516, 830686, 941976, 1969394, 2420681, 2751442, 4150015, 5354867, 7045156, 9590417, 9699457, 10333214, 13427757, 21955652, 31213974, 32743132, 35272742
Offset: 1
56 is in the sequence as 56^3 = 175616 contains 56 in its decimal expansion.
-
Select[Range[5,10^6],Mod[#,10]>0&&SequenceCount[Rest[Drop[IntegerDigits[#^3],-1]],IntegerDigits[#]]>0&] (* James C. McMahon, May 09 2025 *)
A385709
Least prime p such that the decimal expansion of p^2 contains exactly n distinct primes as substrings.
Original entry on oeis.org
11, 5, 23, 61, 73, 239, 487, 523, 569, 3461, 1319, 3373, 8923, 4937, 12619, 11489, 15569, 32189, 105173, 135319, 46619, 56473, 177127, 234161, 295861, 471923, 664319, 2366387, 3183613, 1092389, 3513877, 7702319, 4632077, 10666177, 13977923, 20825939, 35821939
Offset: 1
a(9) = 569 because 569^2 = 323761, which contains 9 distinct primes as substring:{2,3,7,23,37,61,761,3761,23761}, and no prime less than 569 has 9 solutions.
-
b = Table[{}, 9]; Do[d = IntegerDigits[p^2];
t = Union@Select[FromDigits /@ Flatten[Table[Partition[d, k, 1], {k, Length@d}], 1], PrimeQ]; c = Length@t;
If[b[[c]] == {}, b[[c]] = {p, p^2, t, c}], {p, Prime@Range@120}]; b // Grid
Showing 1-3 of 3 results.