A070029 Primes with only prime digits and whose initial, all intermediate and final iterated sums of digits are primes.

2, 3, 5, 7, 23, 223, 227, 353, 2333, 2777, 3323, 7727, 27527, 33377, 33773, 35537, 35573, 35753, 37337, 52727, 53777, 55337, 55373, 55733, 57557, 57737, 57773, 73553, 73757, 75227, 75353, 75377, 75533, 75557, 75773, 77573, 222557, 222773

Offset: 1

Author

Rick L. Shepherd, Apr 21 2002

Keywords

• base
• nonn

Comments

This sequence is the intersection of A062088 and A070027.

Examples

			53777 is a term because 53777 is a prime with only prime digits and 5+3+7+7+7=29, 2+9=11 and 1+1=2 are all prime.
		

Crossrefs

Cf. A070027, A062088 (only first sum of digits is necessarily prime).

Programs

Mathematica

iifpQ[n_]:=AllTrue[NestWhileList[Total[IntegerDigits[#]]&,n,#>9&],PrimeQ]; Select[Prime[Range[20000]],AllTrue[IntegerDigits[#],PrimeQ]&&iifpQ[#]&] (* Harvey P. Dale, Jul 18 2021 *)