cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A351225 a(n) = A276086(n) - n, where A276086 is the primorial base exp-function.

Original entry on oeis.org

1, 1, 1, 3, 5, 13, -1, 3, 7, 21, 35, 79, 13, 37, 61, 135, 209, 433, 107, 231, 355, 729, 1103, 2227, 601, 1225, 1849, 3723, 5597, 11221, -23, -17, -11, 9, 29, 91, -1, 33, 67, 171, 275, 589, 133, 307, 481, 1005, 1529, 3103, 827, 1701, 2575, 5199, 7823, 15697, 4321, 8695, 13069, 26193, 39317, 78691, -11, 37, 85, 231
Offset: 0

Views

Author

Antti Karttunen, Feb 05 2022

Keywords

Comments

Sequence contains no zeros because the parity of A276086(n) is opposite to that of n.

Links

Crossrefs

Cf. A276086, A351226 (positions of negative terms), A351227 (of positive terms).
Cf. also A350074.

Programs

  • Mathematica
    Array[Block[{i, m, n = #, p}, m = i = 1; While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; m - #] &, 64, 0] (* Michael De Vlieger, Feb 05 2022 *)
  • PARI
    A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A351225(n) = (A276086(n)-n);

A351226 Numbers k for which A276086(k) < k, where A276086 is the primorial base exp-function.

Original entry on oeis.org

6, 30, 31, 32, 36, 60, 210, 211, 212, 213, 214, 215, 216, 217, 218, 240, 241, 242, 420, 421, 422, 2310, 2311, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 2320, 2321, 2322, 2323, 2324, 2325, 2328, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2347, 2348, 2352, 2370, 2371, 2372, 2520, 2521, 2522, 2523, 2524, 2526, 2527
Offset: 1

Views

Author

Antti Karttunen, Feb 05 2022

Keywords

Links

Crossrefs

Cf. A002110 (subsequence from its third term 6 onward), A276086, A351227 (complement).
Positions of negative terms in A351225, positions of zeros in A351089.

Programs

  • Mathematica
    Select[Range[2528], Block[{i, m, n = #, p}, m = i = 1; While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; m < #] &] (* Michael De Vlieger, Feb 05 2022 *)
  • PARI
    A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA351226(n) = (A276086(n)

A351229 Numbers k for which A003415(k) >= A276086(k) > k, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

Original entry on oeis.org

2349, 2376, 2400, 2552, 4656, 4680, 4832, 4860, 6936, 6960, 30056, 30080, 30100, 30150, 30256, 30282, 32382, 32384, 32562, 36960, 60080, 510568, 510592, 510996, 511020, 511152, 511176, 511200, 512940, 513096, 513120, 513252, 513272, 515172, 515196, 515352, 515376, 515552, 517448, 517472, 519750, 540636, 540660, 540792
Offset: 1

Views

Author

Antti Karttunen, Feb 05 2022

Keywords

Comments

The terms appear to come in batches dictated by their primorial base expansion (A049345), these terms having only low digit values in that base.

Links

Crossrefs

Cf. A003415, A049345, A276086.
Intersection of A351227 and A351228.
Positions of ones in A351089.

Programs

  • Mathematica
    Select[Range[550000], Block[{i, m, n = #, p}, m = i = 1; While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] >= m > #] &] (* Michael De Vlieger, Feb 05 2022 *)
  • PARI
    A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA351229(n) = { my(u=A276086(n)); ((u > n) && (A003415(n) >= u)); };
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.