A050805 -id:A050805 - cp's OEIS frontend

A050806 Inserting any digit between adjacent digits of prime p produces exactly 1 new prime.

101, 149, 163, 241, 269, 271, 317, 347, 367, 397, 409, 419, 443, 487, 509, 541, 587, 601, 641, 761, 787, 811, 821, 863, 907, 919, 1439, 1481, 1663, 1877, 2089, 2111, 2579, 2593, 2671, 2819, 2971, 3121, 3457, 3463, 3571, 3643, 3659, 3769, 3917, 4001

Offset: 1

Patrick De Geest, Oct 15 1999

			101 yields only one prime using digit '6' -> 1(6)0(6)1 -> prime 16061.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A050674-A050719, A050805.

Cf. A010051, A000040.

import Data.List (intersperse)
a050806 n = a050806_list !! (n-1)
a050806_list = filter ((== 1) . sum . f) a000040_list where
   f p = map (i $ show p) "0123456789"
   i ps d = a010051' (read $ intersperse d ps :: Integer)
-- Reinhard Zumkeller, May 07 2013

aQ[n_]:=Plus@@Boole[PrimeQ[Table[FromDigits[Riffle[IntegerDigits[n],k]],{k,0,9}]]]==1; Select[Prime[Range[5,555]],aQ[#]&] (* Jayanta Basu, May 30 2013 *)

Offset corrected by Reinhard Zumkeller, May 07 2013

A133321 Inserting any (identical) digit between adjacent digits of an odd semiprime k never yields a prime.

Original entry on oeis.org

15, 25, 35, 55, 65, 85, 95, 115, 121, 143, 145, 155, 185, 187, 205, 215, 235, 253, 265, 295, 299, 305, 335, 341, 355, 365, 393, 395, 411, 415, 437, 445, 451, 473, 485, 505, 515, 535, 545, 565, 583, 635, 655, 671, 679, 685, 695, 717, 745, 755, 781, 785, 815

Offset: 1

Jonathan Vos Post, Oct 18 2007

Odd semiprime analog of A050805. Trivially true for any digit if we substitute "even semiprime" for "odd semiprime." Trivially true for any semiprime which is a multiple of 5 (A001750). The nonmultiples of 5 in this sequence begin 121, 143, 187, 253, 299, 341.

			121 is in the sequence because 10201, 11211, 12221, 13231, 14241, 15251, 16261, 17271, 18281, 19291 are all composite.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001358, A001750, A050674-A050719, A050805, A050806.

Select[Select[Range[11,900,2],PrimeOmega[#]==2&],AllTrue[Table[ FromDigits[ Riffle[ IntegerDigits[#],n]],{n,0,9}],CompositeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 07 2018 *)

More terms from R. J. Mathar, Oct 22 2007

cp's OEIS Frontend

A050806 Inserting any digit between adjacent digits of prime p produces exactly 1 new prime.

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