login
This site is supported by donations to The OEIS Foundation.

 

Logo

Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 9-10 2014.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A024770 Right-truncatable primes: every prefix is prime. 47
2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797, 2333, 2339, 2393, 2399, 2939, 3119, 3137, 3733, 3739, 3793, 3797, 5939, 7193, 7331, 7333, 7393, 23333, 23339, 23399, 23993, 29399, 31193 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes in which repeatedly deleting the least significant digit gives a prime at every step until a single digit prime remains. The sequence ends at a(83) = 73939133.

The subsequence which consists of the following "chain" of consecutive right truncatable primes: 73939133, 7393913, 739391, 73939, 7393, 739, 73, 7 yields the largest sum, compared with other chains formed from subsets of this sequence: 73939133 + 7393913 + 739391 + 73939 + 7393 + 739 + 73 + 7 = 82154588. - Alexander R. Povolotsky, Jan 22 2008

Supersequence of A085823, A202263. Subsequence of A012883, A068669. - Jaroslav Krizek, Jan 28 2012

REFERENCES

Roozbeh Hazrat, Mathematica: A Problem-Centered Approach, Springer London 2010, pp. 86-89

LINKS

Jens Kruse Andersen, Table of n, a(n) for n = 1..83 (The full list of terms, taken from link below)

Jens Kruse Andersen, Right-truncatable primes

Angell, I. O. and Godwin, H. J., On Truncatable Primes, Math. Comput. 31, 265-267, 1977.

P. De Geest, The list of 4260 left-truncatable primes

R. Schroeppel, HAKMEM item 33; "Russian Doll Primes", but with a slightly different definition.

Eric Weisstein's World of Mathematics, Truncatable Prime

Index entries for sequences related to truncatable primes

MAPLE

s:=[1, 3, 7, 9]: a:=[[2], [3], [5], [7]]: l1:=1: l2:=4: do for j from l1 to l2 do for k from 1 to 4 do d:=[s[k], op(a[j])]: if(isprime(op(convert(d, base, 10, 10^nops(d)))))then a:=[op(a), d]: fi: od: od: l1:=l2+1: l2:=nops(a): if(l1>l2)then break: fi: od: seq(op(convert(a[j], base, 10, 10^nops(a[j]))), j=1..nops(a)); # Nathaniel Johnston, Jun 21 2011

MATHEMATICA

max = 100000; truncate[p_] := If[PrimeQ[q = Quotient[p, 10]], q, p]; ok[p_] := FixedPoint[ truncate, p] < 10; p = 1; A024770 = {}; While[ (p = NextPrime[p]) < max, If[ok[p], AppendTo[ A024770, p]]]; A024770 (* Jean-François Alcover, Nov 09 2011, after Pari *)

PROG

(Haskell)

import Data.List (inits)

a024770 n = a024770_list !! (n-1)

a024770_list = filter (\x ->

   all (== 1) $ map (a010051 . read) $ tail $ inits $ show x) a038618_list

-- Reinhard Zumkeller, Nov 01 2011

(PARI) {fileO="b024770.txt"; v=vector(100); v[1]=2; v[2]=3; v[3]=5; v[4]=7; j=4; j1=1; write(fileO, "1 2"); write(fileO, "2 3"); write(fileO, "3 5"); write(fileO, "4 7"); until(0, if(j1>j, break); new=1; for(i=j1, j, if(new, j1=j+1; new=0); for(k=1, 9, z=10*v[i]+k; if(isprime(z), j++; v[j]=z; write(fileO, j, " ", z); )))); } \\ Harry J. Smith, Sep 20 2008

(PARI) for(n=2, 31193, v=n; while(isprime(n), c=n; n=(c-lift(Mod(c, 10)))/10); if(n==0, print1(v, ", ")); n=v); \\ Arkadiusz Wesolowski, Mar 20 2014

CROSSREFS

Supersequence of A239747.

Cf. A033664, A024785 (left-truncatable primes), A032437, A020994, A052023, A052024, A052025, A050986, A050987, A069866, A077390 (left-and-right-truncatable primes), A137812 (left-or-right truncatable primes).

Sequence in context: A124673 A024776 A069867 * A038603 A106116 A091727

Adjacent sequences:  A024767 A024768 A024769 * A024771 A024772 A024773

KEYWORD

nonn,base,easy,fini,full,nice

AUTHOR

David W. Wilson

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified September 19 22:34 EDT 2014. Contains 246979 sequences.