A088606 -id:A088606 - cp's OEIS frontend

A088757 a(n) = index of the first occurrence of n in A088606.

2, 5, 7, 8, 26, 40, 134, 160, 107, 172, 35, 79, 739, 267, 137, 1119, 97, 1498, 983, 1404, 2193, 1206, 3262, 369, 3256, 2728, 1406, 3483, 6771, 2226, 12077, 8533, 1890, 9889, 10925, 10935, 3981, 10763, 13030, 16958, 13433, 16369, 47602, 26190, 17115, 33262

Offset: 1

Ray Chandler, Oct 18 2003

nonn

Cf. A088606.

A096915 Smallest prime which when appended to n produces a prime.

Original entry on oeis.org

3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 7, 23, 7, 3, 3, 11, 3, 11, 11, 3, 3, 11, 7, 3, 7, 3, 3, 7, 3, 17, 7, 7, 3, 7, 3, 3, 7, 13, 11, 11, 3, 3, 7, 3, 23, 7, 19, 3, 13, 3, 23, 7, 7, 3, 7, 7, 3, 7, 3, 11, 11, 3, 3, 19, 3, 3, 11, 13, 29, 7, 3, 3, 7, 43, 3, 7, 7, 11, 11, 3, 11, 19, 3, 3, 7, 3, 23, 7, 37, 41

Offset: 1

Bodo Zinser, Aug 18 2004

			a(20)=11 because 11 is prime and 2011 is the smallest prime starting with 20 (2003 is not allowed).

T. D. Noe, Table of n, a(n) for n=1..10000

Cf. A088606, A089777 (the resulting primes). Records: A137177, A144593.

f[n_] := Block[{p = 2, a = IntegerDigits[n]}, While[ !PrimeQ[ FromDigits[ Join[a, IntegerDigits[ Prime[p]]] ]], p++ ]; Prime[p]]; Table[ f[n], {n, 92}] (* Robert G. Wilson v, Aug 20 2004 *)
sp[n_]:=Module[{p=3},While[CompositeQ[n*10^IntegerLength[p]+p],p= NextPrime[ p]];p]; Array[sp,100] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 26 2019 *)

A096915(n) = { local(p=1); until(isprime(eval(Str(n,p=nextprime(p+2)))),);p} \\ M. F. Hasler, Jan 05 2009

More terms from Robert G. Wilson v, Aug 20 2004

Cross-reference to indices of records corrected by M. F. Hasler, Jan 14 2009

A173291 Smallest prime p such that the concatenation of p and prime(n) is a prime, or 0 if no other number exists.

Original entry on oeis.org

0, 2, 0, 3, 2, 3, 3, 7, 2, 2, 3, 3, 2, 7, 3, 3, 3, 7, 3, 2, 3, 3, 2, 3, 3, 5, 7, 5, 3, 2, 7, 2, 2, 19, 11, 7, 19, 3, 3, 9, 2, 3, 3, 7, 5, 37, 7, 31, 5, 3, 5, 2, 13, 2, 3, 41, 2, 3, 31, 2, 7, 2, 3, 2, 3, 11, 3, 13, 2, 7, 11, 3, 13, 3, 19, 2, 2, 13, 17, 37, 5, 13, 5, 3, 139, 5, 3, 3, 3, 3, 2, 5, 7, 3, 3

Offset: 1

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 15 2010

If prime(n) has k digits then a(k) is the smallest prime(m) where 10^k * prime(m) + prime(n) is a prime.

In base 10, no prime can be prefixed to 2 or 5 to make another prime.

			a(2) = 2 because prime(2) = 3, and the concatenation of 2 and 3 gives the prime 23.
a(3) = 0 because prime(3) = 5 and there is no prime to concatenate with to give another prime.
a(4) = 3 because prime(5) = 7 but the concatenation with 2 gives 27 = 3^3, so it has to be 3 in order to give 37, which is prime.

John Derbyshire, Prime obsession. Joseph Henry Press, Washington, DC 2003
Marcus du Sautoy, Die Musik der Primzahlen. Auf den Spuren des groessten Raetsels der Mathematik, Beck, Muenchen 2004
Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005

Cf. A088606, A167764, A168327, A168417, A030469.

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A088757 a(n) = index of the first occurrence of n in A088606.

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A096915 Smallest prime which when appended to n produces a prime.

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A173291 Smallest prime p such that the concatenation of p and prime(n) is a prime, or 0 if no other number exists.

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