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 A246488 Gridgeman pairs in increasing order: pairs of palindromic primes which differ only in their middle digits whose difference is equal to 1. 4
 2, 3, 181, 191, 373, 383, 787, 797, 919, 929, 10501, 10601, 11311, 11411, 12721, 12821, 13831, 13931, 15451, 15551, 16561, 16661, 19891, 19991, 30103, 30203, 30703, 30803, 32323, 32423, 35053, 35153, 38083, 38183, 70507, 70607, 77377, 77477, 78787, 78887, 93139 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It has been conjectured by Norman T. Gridgeman that infinitely many pairs of such primes exist (see second ref.) LINKS Chai Wah Wu, Table of n, a(n) for n = 1..1000 n = 1..100 from Paolo P. Lava. Mauro Fiorentini, Coppie di Gridgeman (in Italian) Mauro Fiorentini, Gridgeman (congettura di) (in Italian) Prime Curios!, 181 EXAMPLE 181 and 191 is a Gridgeman pair because the two numbers are palindromic primes which differ only in their middle digits. Furthermore their middle digits differ only in one unit: 8 and 8 + 1 = 9. The same for 30103 and 30203: middle digits are 1 and 1 + 1 = 2. MAPLE T:=proc(n) local i, x; x:=convert(n, base, 10); add(x[-i]*10^(i-1), i=1..nops(x)) end: P:=proc(q) local a, b, j, k, n; j:=[]; a:=2; for n from 1 to q do if (length(a) mod 2)=1 and T(a)=a then b:=(trunc(a/10^trunc(length(a)/2))); if b mod 10<9 then b:=b+1: b:=b*10^trunc(length(a)/2)+(a mod 10^trunc(length(a)/2)); if isprime(b) then j:=[op(j), a, b]: fi: fi: fi: a:=nextprime(a): od; op(j); end: P(10^4); PROG (PARI) ispal(v) = {for(i=1, #v\2, if (v[i] != v[#v-i+1], return(0)); ); return(1); }; isgpal(p) = {d = digits(p); if ((#d % 2) && ispal(d) && (ic = #d\2 +1) && (d[ic]<9) && (d[ic]++) && isprime(q=subst(Pol(d), x, 10)), q); } lista(nn) = {forprime(p=2, nn, if (q=isgpal(p), print1(p, ", ", q, ", ")); ); } \\ Michel Marcus, Aug 29 2014 (Python) from sympy import isprime A246488 = [2, 3] for n in range(1, 10**4): ....s1 = str(n) ....s2 = s1[::-1] ....for m in range(10-1): ........p1 = int(s1+str(m)+s2) ........p2 = int(s1+str(m+1)+s2) ........if isprime(p1) and isprime(p2): ............A246488.append(p1), A246488.append(p2) . A246488 = sorted(set(A246488)) # Chai Wah Wu, Sep 05 2014 CROSSREFS Cf. A002385. Sequence in context: A042369 A328257 A042701 * A106715 A106817 A233318 Adjacent sequences:  A246485 A246486 A246487 * A246489 A246490 A246491 KEYWORD nonn,base AUTHOR Paolo P. Lava, Aug 28 2014 STATUS approved

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Last modified October 23 20:17 EDT 2019. Contains 328373 sequences. (Running on oeis4.)