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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A001259 A sequence of sorted odd primes 3 = p_1 < p_2 < ... < p_m such that p_i-2 divides the product p_1*p_2*...*p_(i-1) of the earlier primes and each prime factor of p_i-1 is a prime factor of twice the product.

Original entry on oeis.org

3, 5, 7, 17, 19, 37, 97, 113, 257, 401, 487, 631, 971, 1297, 1801, 19457, 22051, 28817, 65537, 157303, 160001
Offset: 1

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Author

N. J. A. Sloane

Keywords

Comments

Old name was: A special sequence of primes.
Holt shows this sequence is complete. - T. D. Noe, Jul 28 2005
This sequence was used by Schinzel (1958) and Schinzel and Wakulicz (1959) to prove that there are at least two solutions k to phi(n+k) = phi(k) for all n <= 8*10^47 and 2*10^58, respectively. - Amiram Eldar, Mar 19 2021

References

  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A007015, A342701.

Extensions

New name, giving a definition, by Jonathan Sondow, Oct 06 2012

A217199 Odd primes p such that 2p-1 is prime and no p is equal to 2q-1 with q in the sequence.

Original entry on oeis.org

3, 7, 19, 31, 79, 97, 139, 199, 211, 229, 271, 307, 331, 337, 367, 379, 439, 499, 547, 577, 601, 607, 619, 691, 727, 811, 829, 937, 967, 1009, 1069, 1171, 1279, 1297, 1399, 1429, 1459, 1531, 1609, 1627, 1759, 1867, 2011, 2029, 2089, 2131, 2179, 2221, 2281
Offset: 1

Views

Author

Michel Marcus, Sep 27 2012

Keywords

Comments

At each step, the smallest possible p is chosen.
These are the primes described in lemma 2 of the paper by Holt. - T. D. Noe, Sep 28 2012
This sequence was used by Holt (2003) to prove that there are at least two solutions k to phi(n+k) = phi(k) for all even n <= 1.38*10^26595411. - Amiram Eldar, Mar 19 2021

Links

Crossrefs

Cf. A007015, A110581, A217198, A342701.

Programs

  • Mathematica
    t = {}; p = 2; Do[p = NextPrime[p]; If[PrimeQ[2*p - 1] && ! MemberQ[2*t - 1, p], AppendTo[t, p]], {PrimePi[2281]}]; t
  • PARI
    intab(val, tab) = {for (ii=1, length(tab),if (tab[ii] == val, return (1);););return(0);}
lista(nn) = {tab = []; for (i=1, nn, len = length(tab); if (len == 0, p = 3, p = nextprime(tab[len]+1)); while (! isprime(2*p-1) || intab((p+1)/2, tab) , p = nextprime(p+1);); tab = concat(tab, p); print1(p, ", "););}
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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