A067227 n is prime and remains prime when its leading digit is replaced by each of 2, 4 and 8.

13, 23, 43, 53, 73, 83, 139, 157, 163, 239, 257, 263, 439, 457, 463, 557, 563, 739, 757, 839, 857, 863, 1297, 1423, 1447, 1663, 1861, 1999, 2111, 2243, 2273, 2297, 2423, 2447, 2663, 2861, 2969, 2999, 4111, 4243, 4273, 4297, 4423, 4447, 4663, 4861, 4969

Offset

1,1

Comments

2, 4 and 8 were chosen because they are powers of 2.

Links

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

Example

53 is prime and so are 23, 43, 83, so 53 is a term of the sequence.

Mathematica

(*replaces the leading digit of n by m*) f[n_, m_] := FromDigits[Flatten[Append[IntegerDigits[m], Drop[IntegerDigits[n], 1]]]]; Select[Range[10^4], PrimeQ[ # ] && PrimeQ[f[ #, 2]] && PrimeQ[f[ #, 4]] && PrimeQ[f[ #, 8]] & ]
Select[Prime[Range[700]], AllTrue[FromDigits/@Table[Join[{i}, Rest[ IntegerDigits[ #]]], {i, {2, 4, 8}}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 04 2017 *)

Crossrefs

Sequence in context: A165350 A236418 A112394 * A240113 A256177 A320752

Adjacent sequences: A067224 A067225 A067226 * A067228 A067229 A067230

Keyword

base,nonn

Author

Joseph L. Pe, Feb 20 2002

Extensions

Offset corrected to 1 and title simplified by M. F. Hasler, Nov 01 2014

Status

approved