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A331869 Numbers n for which R(n) + 4*10^floor(n/2) is prime, where R(n) = (10^n-1)/9 (repunit: A002275). 3
1, 3, 4, 15, 76, 91, 231, 1363, 1714, 1942, 2497 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For n > 1, the corresponding primes are a subset of A105992: near-repunit primes.

In base 10, R(n) + 4*10^floor(n/2) has ceiling(n/2)-1 digits 1, one digit 5, and again floor(n/2) digits 1, except for n = 0. For odd n, this is a palindrome (a.k.a. wing prime, cf. A077783: subsequence of odd terms), for even n the digit 5 is just left to the middle of the number.

See also the variant A331868 where the digit 5 is just to the right of the middle.

LINKS

Table of n, a(n) for n=1..11.

Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).

EXAMPLE

For n = 1, R(1) + 4*10^floor(1/2) = 5 is prime.

For n = 3, R(3) + 4*10^floor(3/2) = 151 is prime.

For n = 4, R(4) + 4*10^floor(4/2) = 1511 is prime.

For n = 15, R(15) + 4*10^floor(15/2) = 111111151111111 is prime.

MATHEMATICA

Select[Range[0, 2500], PrimeQ[(10^# - 1)/9 + 4*10^Floor[#/2]] &]

PROG

(PARI) for(n=0, 9999, ispseudoprime(p=10^n\9+4*10^(n\2))&&print1(n", "))

CROSSREFS

Cf. A105992 (near-repunit primes), A002275 (repunits), A004023 (indices of prime repunits), A011557 (powers of 10).

Cf. A331862, A331861, A331865, A331866 (variants with digit 0, 2, 3 or 4 instead of 5), A331868 (variant with floor(n/2-1) instead of floor(n/2)).

Cf. A077783 (odd terms).

Sequence in context: A135962 A171062 A171061 * A115752 A103095 A041325

Adjacent sequences:  A331866 A331867 A331868 * A331870 A331871 A331872

KEYWORD

nonn,base,hard,more

AUTHOR

M. F. Hasler, Feb 09 2020

STATUS

approved

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Last modified June 2 17:02 EDT 2020. Contains 334787 sequences. (Running on oeis4.)