This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Table[Mod[n!, n^2 + 1], {n, 60}]
a(7) = dp_10(2)*dp_10(3)*dp_10(5)*dp_10(7)*dp_10(11)*dp_10(13)*dp_10(17) = 2*3*5*7*(1*1)*(1*3)*(1*7) = 4410.
a:= proc(n) option remember; `if`(n<1, 1, a(n-1)*mul(
`if`(i=0, 1, i), i=convert(ithprime(n), base, 10)))
end:
seq(a(n), n=1..30); # Alois P. Heinz, Mar 11 2022
Rest[FoldList[Times,1,Times@@Cases[IntegerDigits[#],Except[0]]&/@ Prime[ Range[ 20]]]] (* Harvey P. Dale, Mar 19 2013 *)
f(n) = vecprod(select(x->(x>1), digits(prime(n)))); \\ A101987 a(n) = prod(k=1, n, f(k)); \\ Michel Marcus, Mar 11 2022
from math import prod
from sympy import sieve
def pod(s): return prod(int(d) for d in s if d != '0')
def a(n): return pod("".join(str(sieve[i+1]) for i in range(n)))
print([a(n) for n in range(1, 23)]) # Michael S. Branicky, Mar 11 2022
a(2) = ds_prime(2)(2^4) = ds_3(16) = 1+2+1 = 4; a(6) = ds_prime(6)(6^4) = ds_13(1296) = 7+8+9 = 24.
Table[Total[IntegerDigits[n^4, Prime[n]]], {n, 50}] (* G. C. Greubel, Sep 23 2016 *)
a(n) = vecsum(digits(n^4, prime(n))); \\ Michel Marcus, Sep 24 2016
a(2) = ds_prime(2)(2^5) = ds_3(32) = 1+0+1+2 = 4; a(6) = ds_prime(5)(5^5) = ds_11(3125) = 2+9+3+1 = 15.
Table[Total[IntegerDigits[n^5,Prime[n]]],{n,60}] (* Harvey P. Dale, Jul 19 2013 *)
a(n) = vecsum(digits(n^5, prime(n))); \\ Michel Marcus, Sep 24 2016
a(1)=5, since ds_2(5):ds_3(5)=2:3.
select(t -> convert(convert(t,base,3),`+`)/convert(convert(t,base,2),`+`) = 3/2, [$1..1000]); # Robert Israel, Sep 26 2016
Select[Range[500], 3*Total[IntegerDigits[#, 2]] == 2*Total[IntegerDigits[#, 3]] &] (* G. C. Greubel, Sep 26 2016 *)
isok(n) = 2*vecsum(digits(n, 3)) == 3*vecsum(digits(n, 2)); \\ Michel Marcus, Sep 26 2016
a(2)=12, since ds_2(12)=ds_3(12)=ds_6(12), where ds_x=digital sum base x.
Select[Range[5000], Total[IntegerDigits[#, 2]] == Total[IntegerDigits[#, 3]] == Total[IntegerDigits[#, 6]] &] (* G. C. Greubel, Sep 26 2016 *)
a(7)=4161, since ds_2(4161 )=ds_4(4161 )=ds_8(4161 ), where ds_x=digital sum base x.
Select[Range[500000], Total[IntegerDigits[#, 2]] == Total[IntegerDigits[#, 4]] == Total[IntegerDigits[#, 8]] &] (* G. C. Greubel, Sep 26 2016 *) With[{k = 64}, Rest@ Map[FromDigits[#, k] &, Tuples[{0, 1}, 5]]] (* Michael De Vlieger, Oct 28 2022 *) Select[Range[171*10^5],Length[Union[Total/@IntegerDigits[#,{2,4,8}]]]==1&] (* Harvey P. Dale, May 14 2025 *)
a(n) = fromdigits(binary(n),64); \\ Kevin Ryde, Apr 02 2025
a(2)=1300, since ds_2(1300)=ds_5(1300)=ds_10(1300), where ds_x=digital sum base x.
Select[Range[10000], Total[IntegerDigits[#, 2]] == Total[IntegerDigits[#, 5]] == Total[IntegerDigits[#, 10]] &] (* G. C. Greubel, Sep 27 2016 *)
a(3)=188, since ds_3(188)=ds_4(188)=ds_5(188)=ds_6(188)=8, where ds_x=digital sum base x.
Select[Range[3000], Total[IntegerDigits[#, 3]] == Total[IntegerDigits[#, 4]] == Total[IntegerDigits[#, 5]] == Total[IntegerDigits[#, 6]] &] (* G. C. Greubel, Sep 27 2016 *)
a(2)=12250 since ds_2(12250 )=ds_3(12250 )=ds_5(12250 )=ds_10(12250 )=10, where ds_x=digital sum base x.
Select[Range[32000], Total[IntegerDigits[#, 2]] == Total[IntegerDigits[#, 3]] == Total[IntegerDigits[#, 5]] == Total[IntegerDigits[#, 10]] &] (* G. C. Greubel, Sep 28 2016 *) Select[Range[120000],Length[Union[Total/@IntegerDigits[#,{2,3,5,10}]]]==1&] (* Harvey P. Dale, Mar 30 2024 *)
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