A091632 -id:A091632 - cp's OEIS frontend

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

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

Enoch Haga, Jan 24 2004

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.

G. C. Greubel, Table of n, a(n) for n = 1..1000
Tanya Khovanova, Recursive Sequences
Carlos Rivera, Puzzle 251, Pointer primes, The Prime Puzzles and Problems Connection.
Index entries for linear recurrences with constant coefficients, signature (2).

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.

[3*2^n : n in [1..40]]; // Wesley Ivan Hurt, Jul 17 2020

3*2^Range[1, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)

[3*2^n for n in range(1,51)] # G. C. Greubel, Jan 05 2023

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

Edited and extended by Ray Chandler, Feb 07 2004

A089823 Primes p such that the next prime after p can be obtained from p by adding the product of the digits of p.

Original entry on oeis.org

23, 61, 1123, 1231, 1321, 2111, 2131, 11261, 11621, 12113, 13121, 15121, 19121, 21911, 22511, 27211, 61211, 116113, 131231, 312161, 611113, 1111211, 1111213, 1111361, 1112611, 1123151, 1411411, 1612111, 2111411, 2121131, 3112111

Offset: 1

Joseph L. Pe, Jan 09 2004

I call these primes (multiplicative) "pointer primes", in the sense that such primes p "point" to the next prime after p when the product of the digits of p is added to p. 23 is the only pointer prime < 10^7 which does not contain the digit "1". Are there other pointer primes not containing the digit "1"?

See Prime Puzzle 251 link for several arguments that 23 is the only pointer prime not containing digit "1".

			23 + product of digits of 23 = 29, which is the next prime after 23. Hence 23 belongs to the sequence.

Giovanni Resta, Table of n, a(n) for n = 1..4354 (terms < 10^19)
Carlos Rivera's Prime Puzzles and Problems Connection, Puzzle 251, Pointer primes

Cf. A091628, A091629, A091630, A091631, A091632.

r = {}; Do[p = Prime[i]; q = Prime[i + 1]; If[p + Apply[Times, IntegerDigits[p]] == q, r = Append[r, p]], {i, 1, 10^6}]; r

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

Enoch Haga, Jan 24 2004

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

Tanya Khovanova, Recursive Sequences
Carlos Rivera's Prime Puzzles and Problems Connection, Puzzle 251, Pointer primes
Index entries for linear recurrences with constant coefficients, signature (11,-10).

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

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

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)

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

Enoch Haga, Jan 24 2004

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.

			a(1) = 23 + 6 = 29.

Carlos Rivera's Prime Puzzles and Problems Connection, Puzzle 251, Pointer primes
Index entries for linear recurrences with constant coefficients, signature (13,-32,20).

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

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)

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

Enoch Haga, Jan 24 2004

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.

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

Carlos Rivera's Prime Puzzles and Problems Connection, Puzzle 251, Pointer primes

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

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

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

Edited and extended by Ray Chandler, Feb 07 2004

cp's OEIS Frontend

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

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A089823 Primes p such that the next prime after p can be obtained from p by adding the product of the digits of p.

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A091628 Concatenation of n 2's followed by 3.

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A091630 Numbers n + product of digits associated with A091628.

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A091631 Next prime associated with A091628.

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