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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A080083 Smallest prime p such that there is a gap of 2*prime(n) between p and previous prime.

Original entry on oeis.org

11, 29, 149, 127, 1151, 2503, 1361, 30631, 81509, 44351, 34123, 404671, 265703, 156007, 1101071, 1098953, 1349651, 3117421, 6958801, 10343903, 6034393, 49269739, 83751287, 39390167, 166726561, 107534789, 232424029, 253878617, 327966319, 519653597, 1202442343, 1649329259
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 26 2003

Keywords

Crossrefs

Cf. A000040, A001632, A080082.

Programs

  • PARI
    list(len) = {my(v = vector(len), prv = 3, c = 0, d, i); forprime(p = 5, , d = (p - prv)/2; if(isprime(d), i = primepi(d); if(i < = len && v[i] == 0, c++; v[i] = p; if(c == len, break))); prv = p); v; } \\ Amiram Eldar, Mar 11 2025

Formula

A001632(A000040(n)) < a(n).
a(n) = A080082(n) + 2*A000040(n).

Extensions

a(17)-a(28) from Donovan Johnson, May 30 2010
a(29)-a(32) from Amiram Eldar, Mar 11 2025

A243155 Larger of the two consecutive primes whose positive difference is a cube.

Original entry on oeis.org

3, 97, 367, 397, 409, 457, 487, 499, 691, 709, 727, 751, 769, 919, 937, 991, 1117, 1171, 1201, 1381, 1447, 1531, 1567, 1579, 1741, 1831, 1987, 2011, 2161, 2221, 2251, 2281, 2467, 2539, 2617, 2671, 2707, 2749, 2851, 2887, 2917, 3019, 3049, 3217, 3229, 3457, 3499
Offset: 1

Views

Author

K. D. Bajpai, May 31 2014

Keywords

Comments

Observation: All the terms in this sequence, after a(1), are the larger of the two consecutive primes which have positive difference either 2^3 or 4^3.
Superset of A031927 as the sequence contains for example numbers like 89753, 107441, 288647,.. (with gaps of 4^3...) that are not in A031927. - R. J. Mathar, Jun 06 2014

Examples

			97 is prime and appears in the sequence because 97 - 89 = 8 = 2^3.
397 is prime and appears in the sequence because 397 - 389 = 8 = 2^3.

Links

Crossrefs

Cf. A031927, A123996, A118590, A001632.

Programs

  • Maple
    A243155:= proc() local a; a:=evalf((ithprime(n+1)-ithprime(n))^(1/3)); if a=floor(a) then RETURN (ithprime(n+1)); fi; end: seq(A243155 (), n=1..100);
  • Mathematica
    n = 0; Do[t = Prime[k] - Prime[k - 1]; If[IntegerQ[t^(1/3)], n++; Print[n, " ", Prime[k]]], {k, 2, 15*10^4}]
  • PARI
    s=[]; forprime(p=3, 4000, if(ispower(p-precprime(p-1), 3), s=concat(s, p))); s \\ Colin Barker, Jun 03 2014
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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