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A297960 a(1) = number of 1-digit primes (that is, 4: 2,3,5,7); then a(n) = number of distinct n-digit prime numbers obtained by alternately right- and left-concatenating a digit to the a(n-1) primes obtained in the previous iteration. 2
4, 9, 30, 49, 99, 74, 101, 71, 72, 35, 28, 9, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

No 14-digit numbers can be obtained from the four 13-digit numbers counted by a(13).

LINKS

Table of n, a(n) for n=1..13.

EXAMPLE

1-digit 2-digit 3-digit 4-digit ... 13-digit

------------------------------------------------------------

2 23 223 2237

2239

523 5231

5233

5237

823 8231

8233 6638182333331

8237

29 229 2293

2297

829 8291

8293

8297

929 9293

3 31 131 1319

331 3313

3319

431

631 6311 5981563119937

6317

37 137 1373

337 3371

3373

937 9371

9377

5 53 353 3533

3539

653

853 8537

8539

953 9533

9539

59 359 3593

659 6599

859 8597

8599

7 71 271 2711

2713

2719

571 5711

5717

971 9719

73 173 1733

373 3733

3739

673 6733 8313667333393

6737

773

79 179

379 3793 2682637937713

3797

479 4793

4799

------------------------------------------------------------

a(1) = 4, a(2) = 9, a(3) = 30, a(4) = 49, ..., a(13) = 4.

MATHEMATICA

Block[{b = 10, t}, t = Select[Range[b], CoprimeQ[#, b] &]; TakeWhile[Length /@ Fold[Function[{a, n}, Append[a, If[OddQ[n], Join @@ Map[Function[k, Select[Map[Prepend[k, #] &, Range[9]], PrimeQ@ FromDigits[#, b] &]], Last[a]], Join @@ Map[Function[k, Select[Map[Append[k, #] &, t], PrimeQ@ FromDigits[#, b] &]], Last[a]]]]] @@ {#1, #2} &, {IntegerDigits[Prime@ Range@ PrimePi@b, b]}, Range[2, 16]], # > 0 &]] (* Michael De Vlieger, Jan 20 2018 *)

PROG

(Python)

from sympy import isprime

def alst():

primes, alst = [2, 3, 5, 7], []

while len(primes) > 0:

alst.append(len(primes))

if len(alst)%2 == 0:

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

else:

candidates = set(int(str(p)+d) for p in primes for d in "1379")

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

return alst

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

CROSSREFS

Cf. A050986, A050987, A297961, A298048.

Sequence in context: A241393 A186650 A091658 * A295910 A086688 A309295

Adjacent sequences: A297957 A297958 A297959 * A297961 A297962 A297963

KEYWORD

nonn,full,base,fini

AUTHOR

Seiichi Manyama, Jan 09 2018

STATUS

approved

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Last modified February 6 12:03 EST 2023. Contains 360104 sequences. (Running on oeis4.)