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.

A233692 The smallest prime that produces a set of n primes such that every prime after the first one is equal to the previous plus the product of its nonzero digits.

Original entry on oeis.org

2, 23, 23, 239, 239, 239, 3413, 14249, 524219, 4167379, 324550981, 2589767209, 346333812907
Offset: 1

Views

Author

Carlos Rivera, Dec 14 2013

Keywords

Comments

This sequence was produced as solution to the problem 1270 of Claudio Meller's website (see link).

Examples

			For n=3, initial prime=23, set {23, 29, 47} because 23 -> 23+2*3=29 -> 29+2*9=47.
For n=2 to 9, the sets are
      23,     29;
      23,     29,     47;
     239,    293,    347,    431;
     239,    293,    347,    431,    443;
     239,    293,    347,    431,    443,    491;
    3413,   3449,   3881,   4073,   4157,   4297,   4801;
   14249,  14537,  14957,  16217,  16301,  16319,  16481,  16673;
  524219, 524939, 534659, 550859, 559859, 640859, 649499, 719483, 725531.
		

Crossrefs

Programs

  • PARI
    checkp(p, n) = {ok = isprime(p); for (i=1, n, print1(p, ", "); digs = digits(p); np = p + prod(i=1, #digs, if (d=digs[i], d, 1)); p = np;if (i != n, ok = ok && isprime(p));); ok;} \\ Michel Marcus, Dec 15 2013

Extensions

a(13) from Giovanni Resta, Dec 15 2013

A235680 The smallest first term of a sequence of n primes such that, after the first, each is equal to the previous prime plus the sum of all of its digits, plus the product of all of its nonzero digits.

Original entry on oeis.org

2, 191, 163, 151, 127, 1644997, 36778597, 935715673, 50682890749, 16390560362269, 63334172492839
Offset: 1

Views

Author

Carlos Rivera, Jan 13 2014

Keywords

Comments

The following term produced in each sequence after the n-th is necessarily a composite integer.

Examples

			Example for n=8: a(8)=935715673 because after it the seven primes are 936311069, 936337351, 936490481, 936677149, 938391809, 938811763 and 939029537, with 936311069 = 935715673 + 9*3*5*7*1*5*6*7*3+(9+3+5+7+1+5+6+7+3) and so on...
		

Crossrefs

Extensions

a(9) from Giovanni Resta, Jan 13 2014
a(10)-a(11) from Giovanni Resta, Feb 22 2014

A300326 Sum of the largest possible permutations that can be written without repetition of digits in each base from binary to n+1.

Original entry on oeis.org

0, 2, 23, 251, 3181, 47971, 848638, 17283462, 398650506, 10275193716, 292733747621, 9135147415313, 309906954656231, 11356162260536389, 447015900139452604, 18811774444632517324, 842820629057975778516, 40053081963609542635686, 2012366504118798707101875
Offset: 0

Views

Author

R. J. Cano, Mar 03 2018

Keywords

Comments

It is seems that {a(1), a(2), a(3), a(4)} are the only primes of this form.
From M. F. Hasler, Mar 04 2018: (Start)
For p = 2 and p = 3, a(n) (mod p) is 8- resp. 9-periodic.
For primes 5 <= p <= 23, a(n) (mod p) is p(p-1) periodic. I conjecture this to hold for all p >= 5.
It also appears that the last 4 terms of these periods are (1, 1, 0, 0) (mod p), for any p >= 2, i.e., a(n) is divisible by p at least for k*P-2 <= n <= k*P for any k >= 0, where P is the period length p(p-1) (resp. 8 or 9 for p = 2 and 3).
These properties might allow a proof that a(1..4) are the only primes. However, a(12) = 14231491*21776141, so there is little hope of finding a reasonably sized finite covering set.
(End)

Examples

			Let us consider the numbers: 0[1], 10[2], 210[3], 3210[4], 43210[5], and 543210[6];
Their respective decimal representations are the first six terms of A062813: 0, 2, 21, 228, 2930, 44790. The partial sums for those terms are 0, 2, 23, 251, 3181, and 47971; after 0, the following 4 sums are primes, but 47971 is not prime. The same is true for subsequent partial sums, whence the conjecture in COMMENTS.
		

Crossrefs

Partial sums of A062813.
Cf. A233783 for the occurrence of the ordered triple (2,23,251) in a different context.

Programs

Extensions

Partially edited by M. F. Hasler, Mar 05 2018
Showing 1-3 of 3 results.