A229155 Number of digits of the n-th term of the decimal expansion of e = exp(1) cut into chunks of primes.

1, 1, 649, 1, 1, 2, 29, 1, 1, 2, 1, 1, 1, 53, 1872, 3, 5

Offset: 1

Author

M. F. Hasler, Sep 15 2013

Keywords

• nonn
• base
• more

Comments

Trying to cut the decimal expansion A001113 of e=2.718281828... into "prime chunks", one gets (2, 7, p, 5, 3, 11, q, 7, 3, 61, 3, 3, 2, r, ...) where p, q, r are 649-, 29-, 53-digit primes, respectively. The size of p makes it impossible to register this more fundamental sequence in the OEIS as it is done in A047777 for Pi. This led us to store just the length of the terms in this sequence.

Sequence A121267 is a (not exact) analog for Pi; note that A047777 requires all primes to be distinct, while we allow repetition of 7, 3, 2, ... as seen in the above example. If we did not, the terms following 29 would be 2, 2, 6, 3, 7, 8, 3, 441, 9, 17, ... instead of 1, 1, 2, 1, 1, 1, 53, ...

Links

• Joseph L. Pe, Trying to Write e as a Concatenation of Primes (2009)

Crossrefs

Cf. A007512, A001113, A047658, A064118.

Programs

PARI

default(realprecision,2000);c=exp(1)/10;for(k=1,9e9,ispseudoprime(c\.1^k) & !print1(k,",") & k=0*c=frac(c*10^k))

Extensions

a(15)-a(17) from Jinyuan Wang, Mar 26 2020