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 1-7 of 7 results.

A091629 Product of digits associated with A091628(n). Essentially the same as A007283.

Original entry on oeis.org

6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472
Offset: 1

Views

Author

Enoch Haga, Jan 24 2004

Keywords

Comments

Sequence arising in Farideh Firoozbakht's solution to Prime Puzzle 251 - 23 is the only pointer prime (A089823) not containing digit "1".
The monotonic increasing value of successive product of digits strongly suggests that in successive n the digit 1 must be present.

Links

Crossrefs

Sequences of the form (2*m+1)*2^n: A000079 (m=0), A007283 (m=1), A020714 (m=2), A005009 (m=3), A005010 (m=4), A005015 (m=5), A005029 (m=6), A110286 (m=7), A110287 (m=8), A110288 (m=9), A175805 (m=10), A248646 (m=11), A164161 (m=12), A175806 (m=13), A257548 (m=15).
Cf. A089823, A091628, A091630, A091631, A091632.
Similar to A003945, A042950, A058764, A087009, A081808.

Programs

Formula

a(n) = 3 * 2^n = product of digits of A091628(n).
From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 6*2^(n-1).
a(n) = 2*a(n-1), with a(1) = 6.
G.f.: 6*x/(1-2*x). (End)
E.g.f.: 3*(exp(2*x) - 1). - G. C. Greubel, Jan 05 2023

Extensions

Edited and extended by Ray Chandler, Feb 07 2004

A091628 Concatenation of n 2's followed by 3.

Original entry on oeis.org

23, 223, 2223, 22223, 222223, 2222223, 22222223, 222222223, 2222222223, 22222222223, 222222222223, 2222222222223, 22222222222223, 222222222222223, 2222222222222223, 22222222222222223, 222222222222222223
Offset: 1

Views

Author

Enoch Haga, Jan 24 2004

Keywords

Comments

Sequence arising in Farideh Firoozbakht's solution to Prime Puzzle 251; 23 is the only pointer prime (A089823) not containing the digit "1".

Links

Crossrefs

Cf. A089823, A091629, A091630, A091631, A091632.

Programs

  • Magma
    [ n eq 1 select 23 else 10*Self(n-1)-7: n in [1..17] ];

Formula

a(n) = (10^(n+1) - 1)/9*2 + 1.
a(n) = 10*a(n-1) - 7, with a(1)=23. - Vincenzo Librandi, Nov 16 2010
From Colin Barker, May 06 2012: (Start)
a(n) = 11*a(n-1) - 10*a(n-2).
G.f.: x*(23-30*x)/((1-x)*(1-10*x)). (End)

Extensions

Edited and extended by Ray Chandler, Feb 07 2004

A091630 Numbers n + product of digits associated with A091628.

Original entry on oeis.org

29, 235, 2247, 22271, 222319, 2222415, 22222607, 222222991, 2222223759, 22222225295, 222222228367, 2222222234511, 22222222246799, 222222222271375, 2222222222320527, 22222222222418831, 222222222222615439
Offset: 1

Views

Author

Enoch Haga, Jan 24 2004

Keywords

Comments

Sequence arising in Farideh Firoozbakht's solution to Prime Puzzle 251 - 23 is the only pointer prime (A089823) not containing the digit "1".
The monotonically increasing value of successive product of digits (A091629) strongly suggests that in successive n the digit 1 must be present.

Examples

			a(1) = 23 + 6 = 29.

Links

Crossrefs

Cf. A089823, A091628, A091629, A091631, A091632.

Formula

a(n) = A091628(n) + A091629(n).
From Chai Wah Wu, Feb 12 2021: (Start)
a(n) = 13*a(n-1) - 32*a(n-2) + 20*a(n-3) for n > 3.
G.f.: x*(-120*x^2 + 142*x - 29)/((x - 1)*(2*x - 1)*(10*x - 1)). (End)

Extensions

Edited and extended by Ray Chandler, Feb 07 2004

A091631 Next prime associated with A091628.

Original entry on oeis.org

29, 227, 2237, 22229, 222247, 2222239, 22222253, 222222227, 2222222243, 22222222273, 222222222301, 2222222222243, 22222222222229, 222222222222227, 2222222222222281, 22222222222222301, 222222222222222281
Offset: 1

Views

Author

Enoch Haga, Jan 24 2004

Keywords

Comments

Sequence arising in Farideh Firoozbakht's solution to Prime Puzzle 251 - 23 is the only pointer prime (A089823) not containing the digit "1".
The monotonically increasing value of successive product of digits (A091629) strongly suggests that in successive n the digit 1 must be present.

Examples

			a(1) = nextprime(23+1) = 29.

Links

Crossrefs

Cf. A007918, A089823, A091628, A091629, A091630, A091632.

Programs

  • PARI
    a(n) = nextprime((10^(n+1) - 1)/9*2 + 2); \\ Michel Marcus, Mar 18 2018

Formula

a(n) = A007918(A091628(n)+1).

Extensions

Edited and extended by Ray Chandler, Feb 07 2004

A091632 Excess of n + product of digits over next prime associated with A091628.

Original entry on oeis.org

0, 8, 10, 42, 72, 176, 354, 764, 1516, 3022, 6066, 12268, 24570, 49148, 98246, 196530, 393158, 786406, 1572834, 3145674, 6291440, 12582874, 25165764, 50331634, 100663192, 201326576, 402653180, 805306350, 1610612690, 3221225038
Offset: 1

Views

Author

Enoch Haga, Jan 24 2004

Keywords

Comments

Sequence arising in Farideh Firoozbakht's solution to Prime Puzzle 251 - 23 is the only pointer prime (A089823) not containing the digit "1".
The monotonically increasing value of successive excess (and product of digits (A091629)) strongly suggests that in successive n the digit 1 must be present.

Examples

			a(2) = 235 - 227 = 8.

Links

Crossrefs

Cf. A089823, A091628, A091629, A091630, A091631.

Formula

a(n) = A091630(n) - A091631(n).

Extensions

Edited and extended by Ray Chandler, Feb 07 2004

A125840 Two-sided multiplicative pointer primes.

Original entry on oeis.org

1123, 21911, 3116111, 11413111, 12111331, 14111311, 316111111, 1111131821, 11112119111, 11161211111, 111161111311, 111211231111, 1111112111191, 2111191111111, 11131211113111, 21111121126111, 31111127111111, 111211151611111, 111211222111123, 121132111712111
Offset: 1

Views

Author

Farideh Firoozbakht, Feb 02 2007

Keywords

Comments

Following the definition of multiplicative pointer primes (A089823), I call a prime p a two-sided multiplicative pointer prime if previous_prime(p)=p-P and next_prime(p)=p+P where P is the product of the digits of p.

Examples

			11112119111 is in the sequence because previous_prime(11112119111)
= 11112119111 - 1*1*1*1*2*1*1*9*1*1*1 and next_prime(11112119111)
= 11112119111 + 1*1*1*1*2*1*1*9*1*1*1.

Links

Crossrefs

Cf. A089823, A125841, A127836.

Programs

  • Mathematica
    Do[p=Prime[m];P=Apply[Times,IntegerDigits[p]];If[Prime[m-1]== p-P&&Prime[m+1]==p+P,Print[p]],{m,2,140000000}]

Extensions

a(9)-a(20) from Donovan Johnson, Oct 21 2013

A157655 Zeroless primes p such that the next prime after p can be obtained from p by adding the sum and product of the digits of p.

Original entry on oeis.org

11411, 16111, 1112113, 1151113, 14161111, 14611111, 111115141, 111253111, 115112113, 122112311, 151151111, 211711111, 1111116211, 1121123111, 1121181311, 1211215111, 1412113111, 1416131111, 2111121511, 2111215111
Offset: 1

Views

Author

Cino Hilliard, Mar 03 2009

Keywords

Comments

If we allow a zero digit in p, we generate A089824. One could conjecture that the digit 1 must always appear in the entries of this sequence. The idea for this sequence and the description was motivated by A089823.

Examples

			The digits of 11411 add up to 8. The product of the digits is 4. So 11411+8+4 = 11423, the next prime after 11411. So 11411 is in the sequence.

Links

Crossrefs

Cf. A089823, A089824.

Programs

  • Mathematica
    zpQ[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&NextPrime[n] == n+ Total[ idn]+Times@@idn]; Select[Prime[Range[11*10^7]],zpQ] (* Harvey P. Dale, Jan 14 2016 *)
Showing 1-7 of 7 results.

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