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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A308899 a(n) = largest prime factor of the number with decimal expansion 20305070...0p_n where p_n = n-th prime.

Original entry on oeis.org

2, 29, 131, 33287, 17627, 1754975809, 59218567, 318879703697, 2030507011013017019023, 14400758943354730631369, 1016015647, 32002443156997, 2464082401591041689, 4916481866859605372937116297910511, 2030507011013017019023029031037041043047
Offset: 1

Views

Author

N. J. A. Sloane, Jul 13 2019

Keywords

Comments

The Honaker-Caldwell link gives a(25) =
20305070110130170190230290310370410430470530590
\61067071073079083089097,
with 70 digits.

Examples

			Here are Maple's factorizations of 2, 203, 20305, ... (the factors appear in random order):
2 = (2)
203 = (7)  (29)
20305 = (5)  (31)  (131)
2030507 = (61)  (33287)
2030507011 = (13)  (17627)  (8861)
2030507011013 = (13)  (89)  (1754975809)
2030507011013017 = (59218567)  (34288351)
2030507011013017019 = (7)  (547)  (1663)  (318879703697)

Links

Crossrefs

Inspired by the comment in Bernard Schott's A309101.

Programs

  • Mathematica
    Table[FactorInteger[FromDigits[Flatten[IntegerDigits/@Riffle[Prime[Range[n]],0]]]][[-1,1]],{n,20}] (* Harvey P. Dale, May 09 2021 *)
  • PARI
    pp = 0; forprime (p=2, 47, print1 (vecmax(factor(pp = pp * 10^(1+#digits(p)) + p)[,1]~) ", ")) \\ Rémy Sigrist, Jul 13 2019

Extensions

More terms from Rémy Sigrist, Jul 13 2019

A309566 a(n) is the least prime that can be written as a sequence of primes separated by n single zeros, and where every 0-splitting is prime.

Original entry on oeis.org

307, 130307, 309370307, 30281172370306703
Offset: 1

Views

Author

Michel Marcus, Aug 08 2019

Keywords

Examples

			a(1) = 307 = A309101(1).
130307 is a term since 3, 7, 13, 307, 1303, 130307 are all prime.

Links

Crossrefs

Subsequence of A309101.
Cf. A000040 (primes), A038618 (zeroless primes), A056709 (primes with zeros).

Extensions

a(4) from Daniel Suteu and Giovanni Resta, Aug 09 2019

A309488 Primes whose decimal expansion is of the form d_1+0+d_2+0+d_3+0+...+0+d_k where d_i are digits with 1 <= d_i <= 9, k > 1 and + stands for concatenation.

Original entry on oeis.org

101, 103, 107, 109, 307, 401, 409, 503, 509, 601, 607, 701, 709, 809, 907, 10103, 10301, 10303, 10501, 10601, 10607, 10709, 10903, 10909, 20101, 20107, 20201, 20407, 20507, 20509, 20707, 20807, 20809, 20903, 30103, 30109, 30203, 30307, 30403, 30509, 30703, 30707, 30803, 30809
Offset: 1

Views

Author

Bernard Schott, Aug 04 2019

Keywords

Comments

The terms of this sequence have necessarily an odd number >= 3 of digits.
There is only one term whose digits > 0 are all equal: 101.
The only cyclops primes (A134809) of this sequence are the first 15 terms from 101 to 907.
The first palindromes of this sequence are 101, 10301, 10501, 10601, 30103, 30203, 30403, 30703, 30803, ...
Intersection with A309101 = {503, 10103, 10303, 10903, ...}.

Examples

			103 is the smallest term with two distinct digits > 0.
10607 is the smallest term with three distinct digits > 0.

Crossrefs

Cf. A000040, A002385, A134809, A309101.
Subsequence of A059168 (undulating primes).

Programs

  • Magma
    sol:=[]; m:=1; for p in PrimesInInterval(101,50000) do  v:=Reverse(Intseq(p)); test:=0; for u in [1..#v-1] do if u mod 2 eq 0 and v[u] eq 0 and v[u+1] ne 0 then test:=test+1; end if; end for; if test eq (#v-1)/2 then sol[m]:=p; m:=m+1; end if; end for; sol; // Marius A. Burtea, Aug 04 2019
  • Mathematica
    aQ[n_] := PrimeQ[n] && OddQ[(m = Length[(d = IntegerDigits[n])])] && Flatten@Position[d, ?(# == 0 &)] == Range[2, m, 2]; Select[Range[100, 31000], aQ] (* _Amiram Eldar, Aug 04 2019 *)
  • PARI
    eva(n) = subst(Pol(n), x, 10)
f(n) = my(d=digits(n)); eva(vector(2*#d-1, k, if (k%2, d[1+k\2]))) \\ from Michel Marcus
terms(n) = my(i=0); for(k=10, oo, if(i>=n, break); if(vecmin(digits(k)) > 0, my(iz=f(k)); if(ispseudoprime(iz), print1(iz, ", "); i++)))
/* Print initial 40 terms as follows: */
terms(40) \\ Felix Fröhlich, Aug 08 2019
Showing 1-3 of 3 results.

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

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