A109066 -id:A109066 - cp's OEIS frontend

A155048 Primes p such that number of prime digits of prime(p) = number of nonprime digits of prime(p).

7, 11, 17, 19, 23, 191, 199, 211, 227, 251, 277, 281, 311, 337, 347, 353, 359, 373, 383, 389, 397, 401, 409, 419, 439, 463, 467, 479, 523, 547, 557, 569, 571, 577, 593, 599, 613, 619, 641, 643, 653, 659, 673, 677, 683, 701, 709, 743, 751, 757, 769, 787, 809

Offset: 1

Juri-Stepan Gerasimov, Jan 19 2009

Prime digits are 2, 3, 5 or 7, nonprime digit are 0, 1, 4, 6, 8 or 9.

Cf. A000040, A109066, A141468.

f(n) = #select(isprime, digits(prime(n))); \\ A109066
isok(p) = my(nbp=f(prime(p))); isprime(p) && (2*f(p) == #digits(prime(p)));  \\ Michel Marcus, Feb 18 2021

Corrected (17 and 479 inserted) by R. J. Mathar, May 05 2010

A306890 a(n) is the number of prime digits used in writing out all primes up to and including the n-th prime.

Original entry on oeis.org

1, 2, 3, 4, 4, 5, 6, 6, 8, 9, 10, 12, 12, 13, 14, 16, 17, 17, 18, 19, 21, 22, 23, 23, 24, 24, 25, 26, 26, 27, 29, 30, 32, 33, 33, 34, 36, 37, 38, 40, 41, 41, 41, 42, 43, 43, 44, 47, 50, 52, 55, 57, 58, 60, 63, 65, 66, 68, 71, 72, 74, 76, 78, 79

Offset: 1

Lekraj Beedassy, Mar 15 2019

			We have a(10) = 9 since all primes up to the 10th (2, 3, 5, 7, 11, 13, 17, 19, 23, 29) use the 9 prime digits 2, 3, 5, 7, 3, 7, 2, 3, 2.

Partial sums of A109066. Cf. A068670.

With[{s = IntegerDigits[Prime@ Range@ 64]}, Array[Count[Flatten[s[[1 ;; #]] ], ?PrimeQ] &, Length@ s]] (* _Michael De Vlieger, Mar 27 2019 *)

a(n) = sum(k=1, prime(n), if (isprime(k), #select(x->isprime(x), digits(k)))); \\ Michel Marcus, Mar 23 2019

cp's OEIS Frontend

A155048 Primes p such that number of prime digits of prime(p) = number of nonprime digits of prime(p).

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