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A297961
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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 left- and right-concatenating a digit to the a(n-1) primes obtained in the previous iteration.
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2
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4, 11, 20, 53, 51, 100, 63, 76, 42, 43, 20, 13, 4, 4, 1
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OFFSET
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1,1
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COMMENTS
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No 16-digit numbers can be obtained from the 15-digit number 889292677731979.
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LINKS
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Table of n, a(n) for n=1..15.
Prime Curios, 889292677731979
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EXAMPLE
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1-digit 2-digit 3-digit 4-digit ... 15-digit
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2
3 13 131 2131
6131
137 2137
3137
9137
139 4139
23 233 5233
8233
239 2239
9239
43 431 5431
8431
9431
433 1433
3433
7433
9433
439 1439
9439
53
73 733 1733
3733
4733
6733
9733
739 3739
9739
83 839 5839
8839
9839
5
7 17 173 6173
9173
179 2179
5179
8179
37 373 1373
3373
4373
6373
379 6379
47 479 5479
9479
67 673 3673
4673
6673
7673
677 2677 889292677731979
3677
8677
9677
97 971 2971
6971
8971
977 6977
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a(1) = 4, a(2) = 11, a(3) = 20, a(4) = 53, ..., a(15)= 1.
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MATHEMATICA
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Block[{b = 10, t}, t = Select[Range[b], CoprimeQ[#, b] &]; TakeWhile[Length /@ Fold[Function[{a, n}, Append[a, If[EvenQ[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 *)
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PROG
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(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 == 1:
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
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CROSSREFS
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Cf. A050986, A050987, A297960, A298048.
Sequence in context: A075099 A240784 A345434 * A240155 A161975 A272042
Adjacent sequences: A297958 A297959 A297960 * A297962 A297963 A297964
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KEYWORD
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nonn,full,base,fini
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AUTHOR
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Seiichi Manyama, Jan 09 2018
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STATUS
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approved
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