

A091088


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


2



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
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OFFSET

0,1


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 onedigit 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.


LINKS

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


EXAMPLE

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).


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 *)


PROG

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


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).
Sequence in context: A291634 A098877 A225212 * A335915 A249781 A342041
Adjacent sequences: A091085 A091086 A091087 * A091089 A091090 A091091


KEYWORD

base,easy,nonn,less


AUTHOR

Chuck Seggelin (barkeep(AT)plastereddragon.com), Dec 18 2003


STATUS

approved



