login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A329147 Replace in n each nonzero digit d with prime(d). 3
0, 2, 3, 5, 7, 11, 13, 17, 19, 23, 20, 22, 23, 25, 27, 211, 213, 217, 219, 223, 30, 32, 33, 35, 37, 311, 313, 317, 319, 323, 50, 52, 53, 55, 57, 511, 513, 517, 519, 523, 70, 72, 73, 75, 77, 711, 713, 717, 719, 723, 110, 112, 113, 115, 117, 1111, 1113, 1117, 1119, 1123 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Some properties:

No term has a digit 4, 6 or 8.

No term begins with 9, 10, 12, 15, 29, 39, 59, 79.

If a is regarded as a function a: n --> a(n) from N to N, then

1) a is neither increasing: a(9) > a(10) nor decreasing: a(3) < a(4),

2) a is not injective: a(92) = a(122) = 233,

3) a is not surjective: 4 and 15 are not terms. The integers that are not in this sequence are in A329149 and the integers that are obtained are in A329150, with increasing order.

Some primes remain primes: 2, 3, 5, 7, 19, 59, ...

Some primes become composites: 11, 13, 17, 23, 29, 31, ...

Some composites remain composites: 10, 14, 16, 18, 20, 21, 22,...

Some composites become primes: 4, 6, 8, 9, 12, 15, 24, 25, 26,...

When n > 4 ends respectively with 0, 1 or 3 then a(n) that ends with 0, 2, 5 is composite.

The sequence 9, 99, 999, ..., respectively 12, 1212, 121212, ... generates the same numbers 23, 2323, 232323, ... Analogously, 9, 92, 922, 922, ... and 12, 122, 1222, ... generate the same sequence 23, 233, 2333, 23333, .... For the numbers 91,9191,919191, ... the terms of the sequence are 232, 232232, 232232232, ... so palindromes. - Marius A. Burtea, Nov 07 2019

The numbers 113, 14113, 1441113, 144411113, ... determine the terms 225 = 15^2, 27225 = 165^2, 2772225 = 1665^2, ... (in A191486). The numbers 14, 14000, 14000000, ... determine the terms 27 = 3^3, 27000 = 30^3, 27000000 = 300^3, .... - Marius A. Burtea, Nov 12 2019

LINKS

Metin Sariyar, Table of n, a(n) for n = 0..10000

EXAMPLE

As a(2) = prime(2) = 3, a(5) = prime(5) = 11 and a(8) = prime(8) = 19, a(258)= 31119.

As a(3) = prime(3) = 5, a(0) = 0 and a(7) = prime(7) = 17, hence a(307) = 5017.

MAPLE

a:= n-> (l-> parse(cat(seq(`if`(l[-i]=0, 0, ithprime(l[-i])),

             i=1..nops(l)))))(convert(n, base, 10)):

seq(a(n), n=0..80);  # Alois P. Heinz, Nov 07 2019

MATHEMATICA

p[n_] := If[n > 0, Prime[n], 0]; a[n_] := FromDigits[Flatten @ IntegerDigits @ (p /@ IntegerDigits[n])]; Array[a, 60, 0] (* Amiram Eldar, Nov 06 2019 *)

PROG

(MAGMA) v:=[0, 2, 3, 5, 7, 11, 13, 17, 19, 23]; [0] cat [StringToInteger(&cat[IntegerToString(k): k in Reverse([v[m+1]: m in Intseq(n)])]): n in [1..60]]; // Marius A. Burtea, Nov 07 2019

(PARI) a(n) = if (n, fromdigits(concat(apply(d -> if (d, digits(prime(d)), [0]), digits(n)))), 0) \\ Rémy Sigrist, Nov 07 2019

CROSSREFS

Cf. A000040, A329149, A329150.

Similar to A048380, A048385 and A322131.

Sequence in context: A117322 A242123 A229787 * A048380 A048382 A352584

Adjacent sequences:  A329144 A329145 A329146 * A329148 A329149 A329150

KEYWORD

nonn,base

AUTHOR

Bernard Schott, Nov 06 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 28 19:10 EDT 2022. Contains 354907 sequences. (Running on oeis4.)