

A077785


Odd numbers k such that the palindromic wing number (a.k.a. nearrepdigit palindrome) 7*(10^k  1)/9  2*10^((k1)/2) is prime.


1



3, 15, 27, 117, 259, 507, 3315, 4489, 4875, 15849, 19807, 23799, 36315, 37915, 47331
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OFFSET

1,1


COMMENTS

Original name was "Palindromic wing primes (a.k.a. nearrepdigit palindromes) of the form 7*(10^a(n)1)/92*10^[ a(n)/2 ]."
Prime versus probable prime status and proofs are given in the author's table.
a(16) > 2*10^5.  Robert Price, Jun 23 2017
1 could be considered part of this sequence since the formula evaluates to 5 which is a degenerate form of the nearrepdigit palindrome 777...77577...777 that has zero occurrences of the digit 7.  Robert Price, Jun 23 2017


REFERENCES

C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 199697, pp. 19.


LINKS

Table of n, a(n) for n=1..15.
Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 77...77577...77
Index entries for primes involving repunits.


FORMULA

a(n) = 2*A183180(n) + 1.


EXAMPLE

15 is in the sequence because 7*(10^15  1)/9  2*10^7 = 777777757777777 is prime.


MATHEMATICA

Do[ If[ PrimeQ[(7*10^n  18*10^Floor[n/2]  7)/9], Print[n]], {n, 3, 40000, 2}] (* Robert G. Wilson v, Dec 16 2005 *)


CROSSREFS

Cf. A004023, A077775A077798, A107123A107127, A107648, A107649, A115073, A183174A183187.
Sequence in context: A147041 A002259 A050848 * A222291 A015646 A242571
Adjacent sequences: A077782 A077783 A077784 * A077786 A077787 A077788


KEYWORD

more,nonn,base


AUTHOR

Patrick De Geest, Nov 16 2002


EXTENSIONS

a(15) from Robert Price, Jun 23 2017
Example edited by Jon E. Schoenfield, Jun 23 2017
Name edited by Jon E. Schoenfield, Jun 24 2017


STATUS

approved



