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A333935
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Take a prime p and concatenate it with the next prime after p, q. If the result p||q is prime then take p+q and concatenate the sum to the next prime after q, r. If the result (p+q)||r is prime then take p+q+r and concatenate it to the next prime (s) after r, getting (p+r+r)||s, and so on. a(n) is the least prime for which this process continues for n steps.
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OFFSET
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1,1
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COMMENTS
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i||j denotes the concatenation of the decimal expansions of i and j.
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LINKS
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EXAMPLE
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For p = prime(1) = 2 and prime(2) = 3 the concatenation 2||3 is prime; then 2+3 = 5 and the concatenation of 5 and prime(3) = 5 is 5||5 whicch is not a prime; so the process works for just one step, and a(1) = 2
For p = prime(11)= 31 and prime(12) = 37, the concatenation 31||37 is prime; then 31+37 = 68 and the concatenation of 68 and prime(13) = 41 is 68||41 which is prime; then 68+41 = 109 and the concatenation of 109 and prime(14) = 43 is 109||43 = 31*353 which is not prime; so the process ends after two steps. There is no prime < 31 such that the process continues for 2 steps, so a(2) = 31.
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MATHEMATICA
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catQ[{m_, n_}] := PrimeQ @ FromDigits @ Join[IntegerDigits[m], IntegerDigits[n]]; f[{c_, p_}] := {c + p, NextPrime[p]}; s[p_] := Length @ NestWhileList[f, {0, p}, catQ] - 2; a[n_] := Module[{p = 2}, While[s[p] != n, p = NextPrime[p]]; p]; Array[a, 5] (* Amiram Eldar, Apr 15 2020 *)
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PROG
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(PARI) isok(p, n) = {my(s = p); for (i=1, n, my(q = nextprime(p+1)); if (!isprime(eval(Str(s, q))), return (0)); s += q; p = q; ); return(1); }
a(n) = my(p=prime(1)); while (!isok(p, n), p=nextprime(p+1)); p;
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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