A274833
6-white numbers: partition digits of n^6 into blocks of 6 starting at right; sum of these 6-digit numbers equals n.
Original entry on oeis.org
0, 1, 1208494, 1358344, 1415583, 1538460, 1734265, 1773226, 1818180, 1994707, 2155140, 2187108, 2208493, 2215486, 2272725, 2272726, 2311687, 2318680, 2351350, 2356641, 2358343, 2363634, 2390311, 2402596, 2420874, 2449252, 2454544, 2459835, 2481220, 2500498, 2533168
Offset: 1
1208494^6 = 3115064124992224583219040254156270656 and 3 + 115064 + 124992 + 224583 + 219040 + 254156 + 270656 = 1208494.
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P:=proc(q,h) local a,b,n;
for n from 0 to q do a:=n^h; b:=0; while a>0 do b:=b+(a mod 10^h); a:=trunc(a/10^h); od;
if n=b then print(n); fi; od; end: P(10^6,6);
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k = 6; Select[Range[0, 10^7], Function[n, Total[FromDigits /@ Partition[PadLeft[#, Length@ # + k - Mod[Length@ #, k]], k]] == n &@ IntegerDigits[n^k]]] (* Michael De Vlieger, Jul 08 2016, after Harvey P. Dale at A037045 *)
A277397
Like 4-white numbers but with blocks of 4 starting at left.
Original entry on oeis.org
0, 1, 1000, 11110, 14638, 15628, 17170, 18217, 19305, 19999, 21649, 22320, 25234, 29041, 30195, 31428
Offset: 1
14638^4 = 45912080296849936 and 4591 + 2080+ 2968 + 4993 + 6 = 14638.
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P:=proc(q,h) local a,b,c,d,n; print(0); for n from 1 to q do
a:=n^h; d:=ilog10(n^h)+1; c:=d-h*trunc(d/h); b:=0;
while a>0 do b:=b+(a mod 10^c); a:=trunc(a/10^c); c:=h; od;
if n=b then print(n); fi; od; end: P(10^15,4);
A277398
Like 5-white numbers but with blocks of 5 starting at left.
Original entry on oeis.org
1, 10000, 73440, 95120, 218510, 221220, 222220, 242900, 245610, 289970, 344070
Offset: 1
73440^5 = 2136305413264402022400000 and 21363 + 05413 + 26440 + 20224 + 00000 = 73440.
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P:=proc(q,h) local a,b,c,d,n; print(0); for n from 1 to q do
a:=n^h; d:=ilog10(n^h)+1; c:=d-h*trunc(d/h); b:=0;
while a>0 do b:=b+(a mod 10^c); a:=trunc(a/10^c); c:=h; od;
if n=b then print(n); fi; od; end: P(10^15,5);
A277400
Like 7-white numbers but with blocks of 7 starting at left.
Original entry on oeis.org
0, 1, 1000000, 20585070, 25104356, 25975583, 27483737, 27940490, 27941490, 28133416, 29069509, 32345773, 32482961, 32581773, 33332330, 34310934, 34676272, 35530163, 35707886, 36067139, 41716867, 42163087, 42568703, 44444440, 47745130
Offset: 1
20585070^7 = 1566269305839650871270449961448347855098390430000000 and 1566269 + 3058396 + 5087127 + 0449961 + 4483478 + 5509839 + 0430000 + 000 = 20585070.
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P:=proc(q,h) local a,b,c,d,n; print(0); for n from 1 to q do
a:=n^h; d:=ilog10(n^h)+1; c:=d-h*trunc(d/h); b:=0;
while a>0 do b:=b+(a mod 10^c); a:=trunc(a/10^c); c:=h; od;
if n=b then print(n); fi; od; end: P(10^15,7);
A277399
Like 6-white numbers but with blocks of 6 starting at left.
Original entry on oeis.org
0, 1, 100000, 1705330, 1818180, 1941030, 2046807, 2227770, 2285010, 2414880, 2598400, 2694600, 2727270, 2728270, 2758239, 2760940, 2857140, 2890810, 2979315, 3040660, 3085911, 3317050, 3541014, 3636460, 4543174
Offset: 1
1705330^6 = 24595213291709423201966052256969000000 and 245952 + 132917 + 094232 + 019660 + 522569 + 690000 + 00 = 1705330.
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P:=proc(q,h) local a,b,c,d,n; print(0); for n from 1 to q do
a:=n^h; d:=ilog10(n^h)+1; c:=d-h*trunc(d/h); b:=0;
while a>0 do b:=b+(a mod 10^c); a:=trunc(a/10^c); c:=h; od;
if n=b then print(n); fi; od; end: P(10^15,7);
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Select[Range[0,4544000],Total[FromDigits/@Partition[IntegerDigits[#^6],UpTo[6]]]==#&] (* Harvey P. Dale, Dec 25 2023 *)
A308408
a(n) is the smallest k that is equal to the sum of the digits of k*(k+1)*...*(k+n-1) in base 10^n, or -1 if such a number does not exist.
Original entry on oeis.org
1, 33, -1, 10692, 74016, 1153845, 19999998, 373722624, 3025660311, 39999999996, -1
Offset: 1
a(2) = 33 because 33*34 = 1122 and 11 + 22 = 33.
a(4) = 10692 because 10692*10693*10694*10695 = 13076137707585480 and 5480 + 758 + 1377 + 3076 + 1 = 10692.
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P:=proc(q) local a, b,c,j,k,n,x; c:=1; for n from 1 to q do x:=0:
for k from c to q do a:=mul(j,j=k..k+n-1); b:=0; while a>0 do
b:=b+(a mod 10^n); a:=trunc(a/10^n); od; if k>b then x:=x+1;
else if k
Showing 1-6 of 6 results.
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