A099073
Numbers k such that the concatenation of the first k-1 odd primes in decreasing order is prime.
Original entry on oeis.org
2, 3, 7, 24, 76, 1100
Offset: 1
7 is in the sequence because the first 6 odd primes are 3,5,7,11,13,17 and 17.13.11.7.5.3 is prime (dot between numbers means concatenation).
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Do[If[PrimeQ[(v={};Do[v=Join[v, IntegerDigits[Prime[n-j+1]]], {j, n-1}];FromDigits[v])], Print[n]], {n, 2, 4500}]
Select[Range[1100],PrimeQ[FromDigits[Flatten[IntegerDigits/@ Reverse[ Prime[ Range[ 2,#]]]]]]&] (* Harvey P. Dale, Nov 12 2017 *)
A283561
Numbers k such that the concatenation of the first k nonsquares gives a prime.
Original entry on oeis.org
1, 2, 5, 550, 832, 10431
Offset: 1
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cns[n_]:=FromDigits[Flatten[IntegerDigits[Table[k+Floor[1/2+Sqrt[k]],{k,1,n}]]]]
Select[Table[cns[n],{n,6100}],PrimeQ]
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is(n)=my(s=""); for(k=1,n, s=Str(s, (sqrtint(4*k)+1)\2 + k)); ispseudoprime(eval(s)) \\ Charles R Greathouse IV, Mar 10 2017
A217040
Bases b in which the increasing concatenation of all primes smaller than b forms a prime number.
Original entry on oeis.org
3, 4, 5, 9, 10, 15, 244, 676, 14870, 23526, 35732, 47133, 66878
Offset: 1
2 is the only prime less than 3, and the improper 'concatenation' of this one term is prime, so 3 is in this sequence.
In base 4, the number represented as 23 is 2*4 + 3 = 11, a prime (so 4 is included in the list); the base-5 case, similarly, yields the prime 13, as represented in base 10; 6 is not on the list because 2*6^2+3*6+5=95 is composite; and so on.
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is(n)=isprime(subst(Pol(primes(primepi(n-1))),'x,n)) \\ Charles R Greathouse IV, Sep 26 2012
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from sympy import primerange, isprime
def fromdigits(d, b):
n = 0
for di in d: n *= b; n += di
return n
def ok(b): return isprime(fromdigits([p for p in primerange(1, b)], b))
print([b for b in range(3, 700) if ok(b)]) # Michael S. Branicky, Mar 04 2021
A263959
Number of decimal digits in A069151(n).
Original entry on oeis.org
1, 2, 4, 355, 499, 1171, 1543, 5719
Offset: 1
Cf.
A227529 (Copeland-Erdős constant primes).
Cf.
A227530 (decimal digits in n-th Copeland-Erdős constant prime).
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Cases[FromDigits /@ Rest[FoldList[Join, {}, IntegerDigits[Prime[Range[10^3]]]]], p_?PrimeQ :> IntegerLength[p]]
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p=""; for(n=1, 1e4, p=concat(p, prime(n)); if(ispseudoprime( eval(p)), print1(#Str(p)", "))) \\ Altug Alkan, Oct 30 2015
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