This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A024770 Right-truncatable primes: every prefix is prime. 53
 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 = A023107(10). 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 Can also be seen as a table whose n-th row lists the n-digit terms; row lengths (0 for n >= 9) are given by A050986. The sequence can be constructed starting with the single-digit primes and appending, for each p in the list, the primes within 10*p and 10(p+1), formed by appending a digit to p. - M. F. Hasler, Nov 07 2018 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 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 *) eppQ[n_]:=AllTrue[FromDigits/@Table[Take[IntegerDigits[n], i], {i, IntegerLength[ n]-1}], PrimeQ]; Select[Prime[Range[3400]], eppQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 14 2015 *) 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 (PARI) A024770=vector(9, n, p=concat(apply(t->primes([t, t+1]*10), if(n>1, p)))) \\ The list of n-digit terms, 1 <= n <= 9. Use concat(%) to "flatten" it. - M. F. Hasler, Nov 07 2018 CROSSREFS Supersequence of A085823, A202263. Subsequence of A012883, A068669. - Jaroslav Krizek, Jan 28 2012 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), A254751, A254753. Cf. A237600 for the base-16 analog. Sequence in context: A024776 A069867 A320585 * A038603 A106116 A091727 Adjacent sequences:  A024767 A024768 A024769 * A024771 A024772 A024773 KEYWORD nonn,base,easy,fini,full,nice,tabf,changed AUTHOR STATUS approved

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

Last modified December 16 17:02 EST 2018. Contains 318172 sequences. (Running on oeis4.)