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.

A221847 Number of primes of the form (x+1)^5 - x^5 having n digits.

Original entry on oeis.org

0, 0, 1, 1, 1, 1, 2, 6, 7, 11, 10, 26, 44, 63, 112, 178, 286, 507, 819, 1424, 2385, 4044, 6826, 11591, 19692, 34150, 58171, 99410, 169547, 291195, 500353, 860230, 1482979, 2554281, 4406698
Offset: 0

Views

Author

Vladimir Pletser, Jan 26 2013

Keywords

Comments

Number of primes having n digits and 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. Sequence of number of primes having n digits and of the form (x+1)^5 - x^5 have similar characteristics to similar sequences for natural primes (A006879) and cuban primes (A221792).

A221978 Number of primes of the form (x+1)^7 - x^7 having n digits.

Original entry on oeis.org

0, 0, 1, 0, 1, 1, 3, 1, 1, 2, 4, 4, 7, 9, 12, 14, 29, 31, 45, 62, 71, 117, 175, 231, 331, 454, 634, 948, 1250, 1770, 2506, 3566, 5088, 7192, 10261, 14592, 21168, 30275, 43099, 61336, 87770, 126195, 180957, 258657, 371653, 534391, 767164, 1103259, 1583584, 2276179
Offset: 1

Views

Author

Vladimir Pletser, Feb 02 2013

Keywords

Comments

Number of primes having n digits 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 having n digits and of the form (x+1)^7 - x^7 have similar characteristics to similar sequences for natural primes (A006879), cuban primes (A221792) and primes of the form (x+1)^5 - x^5 (A221847).

Links

Programs

  • Mathematica
    nn = 30; 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]]++]]; t (* T. D. Noe, Feb 04 2013 *)

A221984 Number of primes of the form (x+1)^11 - x^11 having n digits.

Original entry on oeis.org

1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 3, 3, 3, 6, 6, 5, 6, 5, 20, 17, 21, 29, 33, 29, 52, 67, 86, 75, 114, 120, 146, 191, 267, 291, 394, 470, 561, 652, 837, 1063, 1339, 1709, 2018, 2475, 3092, 3680, 4750, 5925, 7295, 9063, 11174, 14034, 17294, 21208
Offset: 9

Views

Author

Vladimir Pletser, Feb 02 2013

Keywords

Comments

Number of primes having n digits 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 having n digits and of the form (x+1)^11 - x^11 have similar characteristics to similar sequences for natural primes (A006879), cuban primes (A221792) and primes of the form (x+1)^p - x^p for p = 5 (A221847) and p = 7 (A221978).

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]]++]]; t (* T. D. Noe, Feb 04 2013 *)
Showing 1-3 of 3 results.

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

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