A091088 a(n) is the minimum odd number that must be appended to n to form a prime.

3, 1, 3, 1, 1, 3, 1, 1, 3, 7, 1, 3, 7, 1, 9, 1, 3, 3, 1, 1, 11, 1, 3, 3, 1, 1, 3, 1, 1, 3, 7, 1, 17, 1, 7, 3, 7, 3, 3, 7, 1, 9, 1, 1, 3, 7, 1, 9, 7, 1, 3, 13, 1, 23, 1, 7, 3, 1, 7, 3, 1, 3, 11, 1, 1, 3, 1, 3, 3, 1, 1, 9, 7, 3, 3, 1, 1, 3, 7, 7, 9, 1, 1, 9, 19, 3, 3, 7, 1, 23, 7, 1, 9, 7, 1, 3, 7, 1, 3, 1, 9, 3

Offset: 0

Author

Chuck Seggelin, Dec 18 2003

Keywords

• base
• easy
• nonn
• less

Comments

This is really a duplicate of A068695. See that entry for existence proof. - N. J. A. Sloane, Nov 07 2020

Note that of course a(n) is not allowed to begin with 0.

Many numbers become prime by appending a one-digit odd number. Some numbers (such as 20, 32, 51, etc.) require a 2 digit odd number (A032352 has these). In the first 100,000 values of n there are only 22 that require a 3 digit odd number (A091089). There probably are some values that require odd numbers of 4 or more digits, but these are likely to be very large.

Examples

			a(0)=3 because 3 is the minimum odd number which when appended to 0 forms a prime (03 = 3 = prime).
a(20)=11 because 11 is the minimum odd number which when appended to 20 forms a prime (201, 203, 205, 207, 209 are all nonprime, 2011 is prime).
		

Links

• Iain Fox, Table of n, a(n) for n = 0..10000
• Index entries for primes involving decimal expansion of n

Crossrefs

Essentially the same as A068695, which is the main entry for this sequence.

Cf. A032352 (a(n) requires at least a 2 digit odd number), A091089 (a(n) requires at least a 3 digit odd number).

Programs

Mathematica

Table[Block[{k = 1}, While[! PrimeQ@ FromDigits[IntegerDigits[n] ~Join~ IntegerDigits[k]], k += 2]; k], {n, 0, 101}] (* Michael De Vlieger, Nov 24 2017 *)

PARI

a(n) = forstep(x=1, +oo, 2, if(isprime(eval(concat(Str(n), x))), return(x))) \\ Iain Fox, Nov 23 2017