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

1,1

Comments

This sequence is the intersection of A062088 and A070027.

Links

Table of n, a(n) for n=1..38.

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A289754 A062088 A343834 * A360497 A368805 A262339

Adjacent sequences: A070026 A070027 A070028 * A070030 A070031 A070032

Keyword

base,nonn

Author

Rick L. Shepherd, Apr 21 2002

Status

approved