A068575 Numbers n such that, as strings, n is a substring of prime(n).

7, 6455, 6456, 6457, 6459, 6460, 6466, 9551, 303027, 440999, 968819, 5517973, 27737957, 93230839, 96664044, 46492090901

Offset: 1

Author

Joseph L. Pe, Mar 26 2002

Keywords

• base
• nonn

Comments

pi(2*10^12) < a(17) <= 426836115943. a(18) <= 732382677641. a(19) <= 4895576080181. [From Donovan Johnson, May 08 2010]

Examples

			Treated as strings, 6455 is a substring of 64553 = Prime(6455), so 6455 belongs to the sequence.
Pairs {n, prime(n)}: {7, 17}, {6455, 64553}, {6456, 64567}, {6457, 64577}, {6459, 64591}, {6460, 64601}, {6466, 64661}, {9551, 99551}, {303027, 4303027}, {440999, 6440999}, {968819, 14968819}, {5517973, 95517973}.
		

Crossrefs

Cf. A067248, A046883, A075902.

Programs

Mathematica

Select[Range[10^6], StringPosition[ToString[Prime[ # ]], ToString[ # ]] != {} &]
Select[Range[97*10^4],SequenceCount[IntegerDigits[Prime[#]],IntegerDigits[#]]>0&] (* The program generates the first 11 terms of the sequence. *) (* Harvey P. Dale, Nov 14 2022 *)

Extensions

More terms from Zak Seidov, Sep 27 2002

Three more terms from Farideh Firoozbakht, Jan 06 2007

a(16) from Donovan Johnson, May 08 2010