A033679 -id:A033679 - cp's OEIS frontend

A046255 a(1) = 5; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

5, 9, 9, 21, 53, 67, 71, 87, 87, 91, 117, 161, 187, 213, 363, 419, 501, 537, 543, 739, 879, 1101, 1329, 1391, 1641, 1939, 2093, 2109, 2331, 2557, 2639, 2697, 2863, 3441, 3441, 4413, 4461, 4479, 4557, 5489, 6033, 6267, 6351, 6973, 7181, 7459, 7679, 8113, 8241

Offset: 1

Patrick De Geest, May 15 1998

nonn

Robert Israel, Table of n, a(n) for n = 1..300

Cf. A069607, A074341, A033680, A033679, A033681, A046254, A046256, A046257, A046258, A046259, A111524.

R:= 5: p:= 5: x:= 5:
for count from 2 to 100 do
  for y from x by 2 do
    if isprime(10^(1+ilog10(y))*p+y) then
      R:= R, y; p:= 10^(1+ilog10(y))*p+y; x:= y;
      break
    fi
od od:
R; # Robert Israel, Nov 22 2020

a[1] = 5; a[n_] := a[n] = Block[{k = a[n - 1], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 49}] (* Robert G. Wilson v, Aug 05 2005 *)

from sympy import isprime
def aupton(terms):
  alst, astr = [5], "5"
  while len(alst) < terms:
    an = alst[-1]
    while an%5 ==0 or not isprime(int(astr + str(an))): an += 2
    alst, astr = alst + [an], astr + str(an)
  return alst
print(aupton(49)) # Michael S. Branicky, May 09 2021

A046259 a(1) = 9; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

Original entry on oeis.org

9, 11, 21, 21, 23, 33, 37, 93, 119, 129, 133, 147, 293, 321, 429, 433, 497, 627, 661, 897, 1161, 1187, 1197, 1711, 1769, 1807, 2097, 2099, 4143, 4149, 4197, 4587, 4587, 5629, 5711, 5889, 6153, 6351, 6399, 6511, 6651, 7179, 7563, 7661, 8071, 8163, 9663

Offset: 1

Patrick De Geest, May 15 1998

nonn

Cf. A069611, A074345, A033680, A033679, A033681, A046254, A046255, A046256, A046257, A046258, A111524.

a[1] = 9; a[n_] := a[n] = Block[{k = a[n - 1], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 48}] (* Robert G. Wilson v, Aug 05 2005 *)

A080155 a(1)=2; a(n) for n>1 is the smallest prime number > a(n-1) such that the concatenation of all previous terms is also prime.

Original entry on oeis.org

2, 3, 11, 31, 47, 229, 251, 577, 857, 859, 911, 1123, 1223, 1297, 1571, 2161, 2417, 2551, 2879, 3319, 5273, 6121, 6947, 7603, 8273, 12721, 12953, 13291, 15683, 16453, 17207, 18133, 20399, 23743, 23909, 25849, 28277, 28879, 35291, 35461, 36107, 43573

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003

See A073640 for the sequence involving concatenation of 2 successive terms, A080153 for 3 successive terms. Primeness is established using Maple's isprime() function, so later terms should be regarded as "probable".

			E.g. a(5)=47 since this is the smallest prime>a(4) which, when concatenated with the concatenation of a(1) to a(4) (=231131), also yields a prime, in this case 23113147.

T. D. Noe, Table of n, a(n) for n = 1..201

Cf. A073640, A080152, A080153, A080154, A080156.

Cf. A033679, A069603, A074338.

with(numtheory): pout := [2]: nout := [1]: for n from 2 to 5000 do: p := ithprime(n): d := parse(cat(seq(pout[i],i=1..nops(pout)),p)): if (isprime(d)) then pout := [op(pout),p]: nout := [op(nout),n]: fi: od: pout;

f[s_List] := Block[{p=NextPrime@s[[-1]], pp=FromDigits@Flatten[IntegerDigits/@s]}, While[!PrimeQ[pp*10^Floor[Log[10,p]+1]+p], p=NextPrime@p]; Append[s,p]]; Nest[f,{2},40]

For any n>1, a(n) is prime and a(n) > a(n-1). a(n) is the smallest prime for which a(1)//a(2)//...//a(n) is prime. // denotes concatenation.

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A046255 a(1) = 5; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A046259 a(1) = 9; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

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A080155 a(1)=2; a(n) for n>1 is the smallest prime number > a(n-1) such that the concatenation of all previous terms is also prime.

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