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.

User: Edmund Algeo

Edmund Algeo's wiki page.

Edmund Algeo has authored 4 sequences.

A301378 a(n) = 10*A007605(n) - 9*A007652(n).

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 11, 13, 17, 19, 23, 37, 41, 47, 49, 59, 61, 67, 73, 77, 83, 89, 91, 101, 103, 107, 109, 31, 43, 47, 49, 53, 59, 61, 71, 77, 83, 89, 91, 97, 101, 103, 113, 37, 41, 43, 47, 61
Offset: 1

Views

Author

Edmund Algeo, Mar 19 2018

Keywords

Comments

Equivalently, a(n) is the sum of all but the last digit of the n-th prime, concatenated with that last digit.
It appears that as the prime number xyzd transformed by (x+y+z)*10 +d; the larger the prime the less frequent the result is prime....

Examples

			For p=1571 (prime), 1+5+7 = 13; 13*10 = 130; 130+1 = 131 (prime).

Links

Crossrefs

Cf. A007605, A007652, A176044.

Programs

  • Maple
    map(t -> 10*convert(convert(t,base,10),`+`)-9*(t mod 10), [seq(ithprime(i),i=1..100)]); # Robert Israel, Mar 25 2018
  • Mathematica
    Array[10 Total@ # - 9 Last@ # &@ IntegerDigits[Prime@ #] &, 67] (* Michael De Vlieger, Apr 27 2018 *)
  • PARI
    a(n) = my(p=prime(n); d=p % 10); sumdigits(p-d)*10+d; \\ Michel Marcus, Mar 23 2018

Formula

Let ...xyzd represent the decimal expansion of prime(n); then a(n) = (... + x + y + z)*10 + d.
a(n) = 10*A007605(n) - 9*A007652(n). - Robert Israel, Mar 25 2018

A229790 Cube roots of difference of consecutive cubes, rounded.

Original entry on oeis.org

1, 2, 3, 3, 4, 4, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24
Offset: 0

Views

Author

Edmund Algeo, Oct 07 2013

Keywords

Examples

			3n^2+3n+1 is the difference of two adjacent cubes, taking the cube root and rounding to a whole number yields an element of the series. 3 cubes is 27, inserting 3 into the formula = 37, 37 plus 27 is 64 the next cube after 27; the cube root of 37 is 3.33222... rounded to 3 is the element in the series.

Crossrefs

Cf. A003215.

Programs

  • Mathematica
    Table[Round[(3*n^2 + 3*n + 1)^(1/3)], {n, 0, 100}] (* T. D. Noe, Oct 22 2013 *)
Round[Surd[#,3]]&/@Differences[Range[0,70]^3] (* Harvey P. Dale, Aug 01 2020 *)
  • PARI
    a(n)=round((3*n*(n+1)+1)^(1/3)) \\ Charles R Greathouse IV, Oct 22 2013

A176246 a(n) = A001223(n+1) - 1.

Original entry on oeis.org

1, 1, 3, 1, 3, 1, 3, 5, 1, 5, 3, 1, 3, 5, 5, 1, 5, 3, 1, 5, 3, 5, 7, 3, 1, 3, 1, 3, 13, 3, 5, 1, 9, 1, 5, 5, 3, 5, 5, 1, 9, 1, 3, 1, 11, 11, 3, 1, 3, 5, 1, 9, 5, 5, 5, 1, 5, 3, 1, 9, 13, 3, 1, 3, 13, 5, 9, 1, 3, 5, 7, 5, 5, 3, 5, 7, 3, 7, 9, 1, 9, 1, 5, 3, 5, 7, 3, 1, 3, 11, 7, 3, 7
Offset: 1

Views

Author

Edmund Algeo, Apr 13 2010

Keywords

Comments

Previous name was: Numbers which added to an odd prime plus one, yield the next prime in the series for primes.
Essentially a duplicate of A046933 and A135732. - T. D. Noe, Oct 23 2013

Crossrefs

Cf. A046933 (number of composites between successive primes).

Programs

  • Mathematica
    Differences[Prime[Range[2, 100]]] - 1 (* Paolo Xausa, Jul 02 2025 *)

Formula

a(n) = A001223(n+1) - 1. - Michel Marcus, Jun 08 2013

Extensions

New name using formula from Michel Marcus, Joerg Arndt, Oct 22 2013

A140528 Sum of digits of Mersenne prime exponents.

Original entry on oeis.org

2, 3, 5, 7, 4, 8, 10, 4, 7, 17, 8, 10, 8, 13, 19, 7, 13, 13, 14, 13, 32, 23, 8, 29, 11, 16, 28, 23, 10, 19, 19, 38, 32, 37, 38, 29, 23, 41, 37, 28, 31, 41, 25, 38, 41, 28, 26, 41
Offset: 1

Views

Author

Edmund Algeo, Jul 03 2008

Keywords

Examples

			Since A000043(15) = 1279, a(15) = 1+2+7+9 = 19. - _Timothy L. Tiffin_, Jul 14 2021

Crossrefs

Cf. A000043, A007953.

Programs

  • Mathematica
    Table[Plus @@ IntegerDigits[e], {e, MersennePrimeExponent[Range[47]]}] (* Amiram Eldar, Jul 16 2021 *)

Formula

a(n) = A007953(A000043(n)). - Michel Marcus, Jul 15 2021

Extensions

a(39)-a(40) corrected by and a(41)-a(47) from Timothy L. Tiffin, Jul 14 2021
a(48) from Amiram Eldar, Oct 18 2024

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