1,1

Last term is a(4260) = 357686312646216567629137 (Angell and Godwin). - Eric W. Weisstein, Dec 11 1999

Can be seen as table whose rows list n-digit terms, 1 <= n <= 25. Row lengths are A050987. - M. F. Hasler, Nov 07 2018

N. J. A. Sloane, Table of n, a(n) for n = 1..4260 (The full list, based on the De Geest web site)

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

James Grime and Brady Haran, 357686312646216567629137, Numberphile video (2018).

Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

Rosetta Code, Programs for finding truncatable primes

Eric Weisstein's World of Mathematics, Truncatable Prime

Chai Wah Wu, On a conjecture regarding primality of numbers constructed from prepending and appending identical digits, arXiv:1503.08883 [math.NT], 2015.

Index entries for sequences related to truncatable primes

a:=[[2], [3], [5], [7]]: l1:=1: l2:=4: for n from 1 to 3 do for k from 1 to 9 do for j from l1 to l2 do d:=[op(a[j]), k]: 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

# second Maple program:

T:= proc(n) option remember; `if`(n=0, "", sort(select(isprime,

      map(x-> seq(parse(cat(j, x)), j=1..9), [T(n-1)])))[])

    end:

seq(T(n), n=1..4);  # Alois P. Heinz, Sep 01 2021

max = 2000; truncate[p_] := If[id = IntegerDigits[p]; FreeQ[id, 0] && (Last[id] == 3 || Last[id] == 7) && PrimeQ[q = FromDigits[ Rest[id]]], q, p]; ok[n_] := FixedPoint[ truncate, n] < 10; p = 5; A024785 = {2, 3, 5}; While[(p = NextPrime[p]) < max, If[ok[p], AppendTo[A024785, p]]]; A024785 (* Jean-François Alcover, Nov 09 2011 *)

d[n_]:=IntegerDigits[n]; ltrQ[n_]:=And@@PrimeQ[NestList[FromDigits[Drop[d[#], 1]]&, n, Length[d[n]]-1]]; Select[Range[1225], ltrQ[#]&] (* Jayanta Basu, May 29 2013 *)

FullList=Sort[Flatten[Table[FixedPointList[Select[Flatten[Table[Range[9]*10^Length@IntegerDigits[#[[1]]] + #[[i]], {i, Length[#]}]], PrimeQ] &, {i}], {i, {2, 3, 5, 7}}]]] (* Fabrice Laussy, Nov 10 2019 *)

(PARI) v=vector(4260); v[1]=2; v[2]=3; v[3]=5; v[4]=7; i=0; j=4; until(i>=j, i++; p=v[i]; P10=10^(1+log(p)\log(10)); for(k=1, 9, z=k*P10+p; if(isprime(z), j++; v[j]=z; ))); s=vector(4260); s=vecsort(v); for(i=1, j, write("b024785.txt", i, " ", s[i]); ); \\

(PARI) is_A024785(n, t=1)={until(t>10*p, isprime(p=n%t*=10)||return); n==p} \\ M. F. Hasler, Apr 17 2014

(PARI) A024785=vector(25, n, p=vecsort(concat(apply(p->select(isprime, vector(9, i, i*10^(n-1)+p)), if(n>1, p))))); \\ Yields the list of rows (n-digit terms, n = 1..25). Use concat(%) to flatten. There are faster variants using matrices (vectorv(9, i, 1)*p+[1..9]~*10^(n-1)*vector(#p, i, 1)) and/or predefined vectors, but they are less concise and this takes less than 0.1 sec. - M. F. Hasler, Nov 07 2018

(Haskell)

import Data.List (tails)

a024785 n = a024785_list !! (n-1)

a024785_list = filter (\x ->

   all (== 1) $ map (a010051 . read) $ init $ tails $ show x) a038618_list

-- Reinhard Zumkeller, Nov 01 2011

(Python)

from sympy import isprime

def alst():

  primes, alst = [2, 3, 5, 7], []

  while len(primes) > 0:

    alst += sorted(primes)

    candidates = set(int(d+str(p)) for p in primes for d in "123456789")

    primes = [c for c in candidates if isprime(c)]

  return alst

print(alst()) # Michael S. Branicky, Apr 11 2021

Supersequence of A240768.

Cf. A033664, A032437, A020994, A024770 (right-truncatable primes), A052023, A052024, A052025, A050986, A050987, A077390 (left-and-right truncatable primes), A137812 (left-or-right truncatable primes), A254753.

Sequence in context: A042993 A308711 A033664 * A069866 A125772 A233282

Adjacent sequences:  A024782 A024783 A024784 * A024786 A024787 A024788

nonn,base,easy,fini,full,tabf

David W. Wilson

approved