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A091088 a(n) is the minimum odd number that must be appended to n to form a prime. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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.

LINKS

Iain Fox, Table of n, a(n) for n = 0..10000

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 * A249781 A115627 A128218

Adjacent sequences:  A091085 A091086 A091087 * A091089 A091090 A091091

KEYWORD

base,easy,nonn

AUTHOR

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

STATUS

approved

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Last modified October 16 18:38 EDT 2019. Contains 328102 sequences. (Running on oeis4.)