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 A024770 Right-truncatable primes: every prefix is prime. 56
 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 I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977. Patrick 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 (Python) from sympy import primerange p = lambda x: list(primerange(x, x+10)); A024770 = p(0); i=0 while i

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)