A306395 Primes g such that 8*g + 2*p is a primorial for some twin prime p.
2, 3, 11, 19, 23, 31, 37, 79, 83, 97, 113, 131, 139, 157, 173, 181, 191, 211, 229, 233, 239, 241, 251, 263, 271, 281, 293, 331, 337, 359, 367, 379, 419, 431, 439, 449, 503, 541, 547, 601, 607, 619, 641, 653, 659, 661, 691, 701, 719, 727, 743, 761, 769, 809
Offset: 1
Keywords
Examples
n | b# = 8 * g + 2 * p greater or lesser --+---------------------------------------------- 1 | 5# = 8 * 2 + 2 * 7 greater 2 | 5# = 8 * 3 + 2 * 3 lesser 3 | 7# = 8 * 11 + 2 * 61 greater 4 | 7# = 8 * 19 + 2 * 29 lesser 5 | 7# = 8 * 23 + 2 * 13 greater 6 | 11# = 8 * 31 + 2 * 1031 lesser
Links
- Michael G. Kaarhus, Table of n, a(n) for n = 0..250
- Michael G. Kaarhus, Additional data
Programs
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CALC
#!/usr/bin/calc -q -f global b=5, chck=list(), g=1, gt, mg30=2, mg6, mp30=7, n=1, oar=pfact(b)/2, tpr=7, ts='greatr', fmt = "%4d%s%5d%s%7d%7d%9d%11s%s%d\n"; define bookem(an) { mp30=mod(tpr, 30); printf(fmt, n, '.', b, '#', an, mg30, mp30, ts, ' ', tpr); n++; append(chck, an); return(an); } define incg() { top: g=nextprime(g); mg6=mod(g, 6); mg30=mod(g, 30); if (mg30 == 13 || mg30 == 17) {goto top;} else {gt=g*4; return(mg30);} } define incb(p) {b=nextprime(p); oar=pfact(b)/2; return(b);} print; printf(fmt, 'n', '.', 'b', '#', 'g', 'g%30', 'twin%30', 'twin type', ' ', 'twin prime'); print '----------------------------------------------------------'; for (i=0; i<=1; i++) {g=nextprime(g); bookem(g); tpr=3; ts='lesser'; mg30=3;} b=incb(b); while (g <= b) {incg();} while (n <= 35) { while (g > b) { tpr=oar-gt; if (tpr <= 7) {incb(b); continue;} if (ptest(tpr, 200)) { if (mg6 == 1 && ptest(tpr+2, 200)) { ts='lesser'; bookem(g); break; } else {if (ptest(tpr-2, 200)) { ts='greatr'; bookem(g); break; } } } incb(b); } incg(); while (oar-gt > 0) {b=prevprime(b); oar=pfact(b)/2;} } print; chs=size(chck)-1; for (i=0; i <= chs; i++) {print i+1, chck[[i]];}
Comments