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.

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A275687 Difference between the smallest 10^n-digit member of a sexy prime quadruple and 10^(10^n - 1), or 0 if no such 10^n-digit number exists.

Original entry on oeis.org

0, 9561, 70495851, 465621162291
Offset: 0

Views

Author

Arkadiusz Wesolowski, Aug 05 2016

Keywords

Examples

			a(0) = 0 because (5, 11, 17, 23, 29) is a sexy prime 5-tuple and this is the only sexy prime 5-tuple.
a(1) = 9561 because 10^9+9561 is the smallest 10-digit member of a sexy prime quadruple. The quadruple is (10^9+9561, 10^9+9567, 10^9+9573, 10^9+9579).

Crossrefs

Cf. A023201, A023271, A133449.

Formula

Conjecture: a(n) = A133449(10^(n-1)) for n >= 1. - Jason Yuen, Mar 07 2025

A297847 Sexiness of p = prime(n): number of iterations of the function f(x) = x + 6 that leave p prime.

Original entry on oeis.org

0, 0, 4, 2, 3, 1, 2, 0, 1, 0, 2, 1, 3, 0, 2, 1, 0, 3, 2, 0, 1, 0, 1, 0, 2, 2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 1, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 1, 0, 0, 3, 2, 1, 0, 2, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 2, 0, 1, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0
Offset: 1

Views

Author

Felix Fröhlich, Jan 07 2018

Keywords

Comments

a(n) > 0 iff p is a term of A023201.
a(n) = 0 iff p is a term of A140555.
a(n) = 2 iff p is a term of A046118.
a(n) > 2 iff p is a term of A023271.
a(n) < 4 except for n = 3. Proof: The last digits of the numbers in the progression repeat 1, 7, 3, 9, 5, 1, 7, 3, 9, 5, ..., so a(n) is at most 4, which only happens for p = 5, since A007652(n) = 5 only for n = 3.

Examples

			For n = 13: prime(13) = 41 and 41 remains prime through exactly 3 iterations of f(x) = x + 6, since 47, 53 and 59 are prime, but 65 is composite, so a(13) = 3.

Links

Crossrefs

Cf. A023201, A023271, A046118, A140555.

Programs

  • Mathematica
    Array[-2 + Length@ NestWhileList[# + 6 &, Prime@ #, PrimeQ] &, 105] (* Michael De Vlieger, Jan 11 2018 *)
  • PARI
    a(n) = my(p=prime(n), x=p, i=0); while(1, x=x+6; if(!ispseudoprime(x), return(i), i++))
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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