A070278 Smallest prime > 2n+1 beginning and ending with 2n+1, or 0 if no such prime exists.

11, 313, 0, 727, 919, 11311, 13313, 0, 17117, 19219, 21121, 23623, 0, 27127, 29129, 31231, 33533, 0, 37337, 39139, 41141, 43543, 0, 47147, 49549, 51151, 53353, 0, 57457, 59159, 61261, 63463, 0, 67567, 692269, 71171, 73673, 0, 77377, 79279

Offset

0,1

Comments

No such prime exists if n is even or divisible by 5. It is not until n = 69 that it necessary to insert more than one digit. The next few examples are 99, 101, 103, 123, 157, 181 & 199.

Insignificant leading 0's in the inserted value are not permitted, otherwise we would have a(34) = 690269. - Sean A. Irvine, Jun 06 2024

Links

Table of n, a(n) for n=0..39.

Mathematica

f[n_] := Block[{a = IntegerDigits[n]}, If[ Mod[n, 5] == 0, Return[0], If[ p = FromDigits[ Join[a, a]]; PrimeQ[p], Return[p], k = 0; While[p = FromDigits[ Join[a, IntegerDigits[k], a]]; !PrimeQ[p], k++ ]]; p]]; Table[ f[n], {n, 1, 89, 2}]

Crossrefs

Sequence in context: A185071 A060495 A251589 * A090272 A090271 A267753

Adjacent sequences: A070275 A070276 A070277 * A070279 A070280 A070281

Keyword

base,nonn

Author

Amarnath Murthy, May 07 2002

Extensions

Edited by N. J. A. Sloane, Vladeta Jovovic and Robert G. Wilson v, May 09 2002

Status

approved