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!)
A240624 Prime numbers n such that replacing each digit d in the decimal expansion of n with d^d produces a prime. Zeros are not allowed. 2
11, 13, 17, 31, 53, 61, 71, 79, 151, 167, 229, 233, 251, 263, 311, 313, 331, 337, 349, 367, 389, 419, 443, 673, 751, 947, 971, 991, 1433, 1531, 1699, 1733, 1993, 2111, 2141, 2153, 2221, 2333, 2393, 2521, 2833, 2963, 3137, 3167, 3323, 3343, 3371, 3389, 3391 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A240623.

If zeros are counted with the convention 0^0 = 1, we find the additional primes 409, 2011, 2027, 2053, 2063, 2081, 2503, 3037, 3061, 3067, 4093, 6029, 6079, 6203, 7001, 8011, 8101, 8807, 9043, 9403, 10103, 10141, 10211, 10321, 10513, 10663, 11003, 11027, 11503, 12037,...

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

EXAMPLE

263 is in the sequence because 263 becomes 44665627 which is also prime, where 44665627 is the concatenation (2^2, 6^6, 3^3) = (4, 46656, 27).

MATHEMATICA

lst={}; f[n_]:=Block[{a=IntegerDigits[n], b="", k=1, l}, l=Length[a]; While[k<l+1, b=StringJoin[b, ToString[a[[k]]^a[[k]]]]; k++]; ToExpression[b]]; Do[If[PrimeQ[f[Prime[n]]], AppendTo[lst, Prime[n]]], {n, 1, 600}]; lst

ddQ[n_]:=Module[{idn=IntegerDigits[n]}, !MemberQ[idn, 0]&&PrimeQ[FromDigits[ Flatten[ IntegerDigits/@ (idn^idn)]]]]; Select[Prime[Range[500]], ddQ] (* Harvey P. Dale, Dec 16 2014 *)

CROSSREFS

Cf. A068492, A240623.

Sequence in context: A325870 A090236 A240623 * A032502 A209871 A347702

Adjacent sequences:  A240621 A240622 A240623 * A240625 A240626 A240627

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Apr 09 2014

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 May 21 05:37 EDT 2022. Contains 353889 sequences. (Running on oeis4.)