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.

A221848 Partial sums of primes equal (x+1)^5 - x^5.

Original entry on oeis.org

31, 242, 4893, 65944, 437225, 1161126, 2964127, 5825588, 10154739, 15080020, 22166471, 30110772, 44945803, 64557704, 87939735, 132059086, 186723797, 273272598, 371065129, 533543630, 723425661, 990642712, 1283752673, 1590492954, 2080592455
Offset: 1

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Author

Vladimir Pletser, Jan 26 2013

Keywords

Comments

Partial sums of primes equal to the difference of two consecutive fifth powers (x+1)^5 - x^5 = 5x(x+1)(x^2+x+1)+1 (A121616). Values of x = A121617. Number of primes equal (x+1)^5 - x^5 < 10^(n) in A221846. Partial sums of number of primes of the form (x+1)^5 - x^5 have similar characteristics to similar sequences for natural primes (A007504) and cuban primes (A221793).

Links

Programs

  • Mathematica
    Accumulate[Select[#[[2]]-#[[1]]&/@Partition[Range[100]^5,2,1],PrimeQ]] (* Harvey P. Dale, Mar 29 2013 *)

Extensions

More terms from Harvey P. Dale, Mar 29 2013

A221977 Number of primes of the form (x+1)^7 - x^7 less than 10^n.

Original entry on oeis.org

0, 0, 1, 1, 2, 3, 6, 7, 8, 10, 14, 18, 25, 34, 46, 60, 89, 120, 165, 227, 298, 415, 590, 821, 1152, 1606, 2240, 3188, 4438, 6208, 8714, 12280, 17368, 24560, 34821, 49413, 70581, 100856, 143955, 205291, 293061, 419256, 600213, 858870, 1230523, 1764914, 2532078
Offset: 1

Views

Author

Vladimir Pletser, Feb 02 2013

Keywords

Comments

Number of primes less than 10^n and equal to the difference of two consecutive seventh powers (x+1)^7 - x^7 = 7x(x+1)(x^2+x+1)^2+1 (A121618). Values of x = A121619 - 1. Sequence of number of primes less than 10^n and of the form (x+1)^7 - x^7 have similar characteristics to similar sequences for natural primes (A006880), cuban primes (A113478) and primes of the form (x+1)^5 - x^5 (A221846).

Links

Programs

  • Mathematica
    nn = 20; t = Table[0, {nn}]; n = 0; While[n++; p = (n + 1)^7 - n^7; p < 10^nn,If[PrimeQ[p], m = Ceiling[Log[10, p]]; t[[m]]++]]; Accumulate[t] (* T. D. Noe, Feb 04 2013 *)

A221983 Number of primes of the form (x+1)^11 - x^11 less than 10^n.

Original entry on oeis.org

1, 2, 3, 3, 4, 4, 4, 4, 5, 6, 6, 8, 9, 9, 9, 12, 15, 18, 24, 30, 35, 41, 46, 66, 83, 104, 133, 166, 195, 247, 314, 400, 475, 589, 709, 855, 1046, 1313, 1604, 1998, 2468, 3029, 3681, 4518, 5581, 6920, 8629, 10647, 13122, 16214, 19894, 24644, 30569, 37864, 46927
Offset: 9

Views

Author

Vladimir Pletser, Feb 02 2013

Keywords

Comments

Number of primes less than 10^n and equal to the difference of two consecutive eleventh powers (x+1)^11 - x^11 = 11x(x+1)(x^2+x+1)( x(x+1)(x^2+x+1)(x^2+x+3)+1) + 1 (A189055). Values of x = A211184. Sequence of number of primes less than 10^n and of the form (x+1)^11 - x^11 have similar characteristics to similar sequences for natural primes (A006880), cuban primes (A113478) and primes of the form (x+1)^p - x^p for p = 5 (A221846) and p = 7 (A221977).

Links

Programs

  • Mathematica
    nn = 40; t = Table[0, {nn}]; n = 0; While[n++; p = (n + 1)^11 - n^11; p < 10^nn, If[PrimeQ[p], m = Ceiling[Log[10, p]]; t[[m]]++]]; Accumulate[t] (* T. D. Noe, Feb 04 2013 *)
Showing 1-3 of 3 results.

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