A137443 First n-digit prime in consecutive digits of e.

7, 71, 281, 4523, 74713, 904523, 6028747, 72407663, 360287471, 7427466391, 75724709369, 749669676277, 8284590452353, 99959574966967, 724709369995957, 2470936999595749, 28459045235360287, 571382178525166427

Offset

1,1

Comments

If the "2" at the beginning of e is included, the only values for n <= 1000 that change are a(1) = 2, a(3) = 271 and a(85) = 2718281828459045235360287471352662497757247093699959574966967627724076630353547594571.

For another version starting with 2 see A095935. - Omar E. Pol, Oct 24 2011

Links

Dan Drake, Table of n, a(n) for n = 1..1000

Pegg, E. Jr. and Weisstein, E. W. Mathematica's Google Aptitude. MathWorld Headline news, Oct 13, 2004.

Example

7427466391 is the first 10-digit prime found in consecutive digits of e, so a(10) = 7427466391.

Prog

(Sage)
def a(digits):
    bits = 0
    pos = 0
    while True:
        bits += (digits * 4) + 50
        decimals = RealField(bits, rnd='RNDZ')(exp(1)).frac().str()[2:]
        for s in range(pos, len(decimals) - digits + 1):
            if decimals[s] != '0':
                i = Integer(decimals[s:s+digits])
                if i.is_prime():
                    return i
        pos = len(decimals) - digits + 1

Crossrefs

Cf. A095926.

Cf. A001113, A095935. - Omar E. Pol, Oct 24 2011

Sequence in context: A201261 A069634 A069619 * A362106 A107601 A175863

Adjacent sequences: A137440 A137441 A137442 * A137444 A137445 A137446

Keyword

base,nonn

Author

Dan Drake, Apr 18 2008

Status

approved