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 A077785 Odd numbers k such that the palindromic wing number (a.k.a. near-repdigit palindrome) 7*(10^k - 1)/9 - 2*10^((k-1)/2) is prime. 1
 3, 15, 27, 117, 259, 507, 3315, 4489, 4875, 15849, 19807, 23799, 36315, 37915, 47331 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Original name was "Palindromic wing primes (a.k.a. near-repdigit palindromes) of the form 7*(10^a(n)-1)/9-2*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 near-repdigit 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, 1996-97, pp. 1-9. LINKS Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's) Makoto Kamada, Prime numbers of the form 77...77577...77 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, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187. 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

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