A077798 Palindromic wing primes (a.k.a. near-repdigit palindromic primes) of the general form r*(10^d - 1)/9 + (m-r)*10^floor(d/2) where d is the number of digits (an odd number > 1), r is the repeated digit, and m (different from r) is the middle digit.

101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 11311, 11411, 33533, 77377, 77477, 77977, 1114111, 1117111, 3331333, 3337333, 7772777, 7774777, 7778777, 111181111, 111191111, 777767777, 77777677777, 99999199999, 1111118111111

Offset: 1

Author

Patrick De Geest, Nov 16 2002

Keywords

• nonn
• base

Comments

Prime versus probable prime status and proofs are given in the author's table.

References

• C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..124
• Patrick De Geest, PWP Reference Table
• Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

Crossrefs

Cf. A077775-A077797.

Programs

Magma

a:=[]; for d in [3..13 by 2] do for r in [1..9] do for m in [0..9] do if m ne r then t:=r*((10^d-1) div 9) + (m-r)*10^(d div 2); if IsPrime(t) then a[#a+1]:=t; end if; end if; end for; end for; end for; a; // Jon E. Schoenfield, Nov 04 2018

Extensions

Offset corrected by Arkadiusz Wesolowski, Sep 13 2011

Name edited and one more term added by Jon E. Schoenfield, Nov 03 2018